Right Triangles - ACT Math
Card 0 of 810
In the figure below, right triangle 
has a hypotenuse of 6. If 
and 
, find the perimeter of the triangle 
.
In the figure below, right triangle
How do you find the perimeter of a right triangle?
There are three primary methods used to find the perimeter of a right triangle.
- When side lengths are given, add them together.
- Solve for a missing side using the Pythagorean theorem.
- If we know side-angle-side information, solve for the missing side using the Law of Cosines.
Method 1:
This method will show you how to calculate the perimeter of a triangle when all sides lengths are known. Consider the following figure:
If we know the lengths of sides 
, 
, and 
, then we can simply add them together to find the perimeter of the triangle. It is important to note several things. First, we need to make sure that all the units given match one another. Second, when all the side lengths are known, then the perimeter formula may be used on all types of triangles (e.g. right, acute, obtuse, equilateral, isosceles, and scalene). The perimeter formula is written formally in the following format:
Method 2:
In right triangles, we can calculate the perimeter of a triangle when we are provided only two sides. We can do this by using the Pythagorean theorem. Let's first discuss right triangles in a general sense. A right triangle is a triangle that has one 
angle. It is a special triangle and needs to be labeled accordingly. The legs of the triangle form the 
angle and they are labeled 
and 
. The side of the triangle that is opposite of the 
angle and connects the two legs is known as the hypotenuse. The hypotenuse is the longest side of the triangle and is labeled as 
.
If a triangle appears in this format, then we can use the Pythagorean theorem to solve for any missing side. This formula is written in the following manner:
We can rearrange it in a number of ways to solve for each of the sides of the triangle. Let's rearrange it to solve for the hypotenuse, 
.
Rearrange and take the square root of both sides.
Simplify.
Now, let's use the Pythagorean theorem to solve for one of the legs, 
.
Subtract 
from both sides of the equation.
Take the square root of both sides.
Simplify.
Last, let's use the Pythagorean theorem to solve for the adjacent leg, 
.
Subtract 
from both sides of the equation.
Take the square root of both sides.
Simplify.
It is important to note that we can only use the following formulas to solve for the missing side of a right triangle when two other sides are known:
After we find the missing side, we can use the perimeter formula to calculate the triangle's perimeter.
Method 3:
This method is the most complicated method and can only be used when we know two side lengths of a triangle as well as the measure of the angle that is between them. When we know side-angle-side (SAS) information, we can use the Law of Cosines to find the missing side. In order for this formula to accurately calculate the missing side we need to label the triangle in the following manner:
When the triangle is labeled in this way each side directly corresponds to the angle directly opposite of it. If we label our triangle carefully, then we can use the following formulas to find missing sides in any triangle given SAS information:
After, we calculate the right side of the equation, we need to take the square root of both sides in order to obtain the final side length of the missing side. Last, we need to use the perimeter formula to obtain the distance of the side lengths of the polygon.
Solution:
Now, that we have discussed the three methods used to calculate the perimeter of a triangle, we can use this information to solve the problem.
First, we need to use the Pythagorean theorem to solve for 
.
Because we are dealing with a triangle, the only valid solution is 
because we can't have negative values.
After you have found 
, plug it in to find the perimeter. Remember to simplify all square roots!
How do you find the perimeter of a right triangle?
There are three primary methods used to find the perimeter of a right triangle.
- When side lengths are given, add them together.
- Solve for a missing side using the Pythagorean theorem.
- If we know side-angle-side information, solve for the missing side using the Law of Cosines.
Method 1:
This method will show you how to calculate the perimeter of a triangle when all sides lengths are known. Consider the following figure:
If we know the lengths of sides
Method 2:
In right triangles, we can calculate the perimeter of a triangle when we are provided only two sides. We can do this by using the Pythagorean theorem. Let's first discuss right triangles in a general sense. A right triangle is a triangle that has one
If a triangle appears in this format, then we can use the Pythagorean theorem to solve for any missing side. This formula is written in the following manner:
We can rearrange it in a number of ways to solve for each of the sides of the triangle. Let's rearrange it to solve for the hypotenuse,
Rearrange and take the square root of both sides.
Simplify.
Now, let's use the Pythagorean theorem to solve for one of the legs,
Subtract
Take the square root of both sides.
Simplify.
Last, let's use the Pythagorean theorem to solve for the adjacent leg,
Subtract
Take the square root of both sides.
Simplify.
It is important to note that we can only use the following formulas to solve for the missing side of a right triangle when two other sides are known:
After we find the missing side, we can use the perimeter formula to calculate the triangle's perimeter.
Method 3:
This method is the most complicated method and can only be used when we know two side lengths of a triangle as well as the measure of the angle that is between them. When we know side-angle-side (SAS) information, we can use the Law of Cosines to find the missing side. In order for this formula to accurately calculate the missing side we need to label the triangle in the following manner:
When the triangle is labeled in this way each side directly corresponds to the angle directly opposite of it. If we label our triangle carefully, then we can use the following formulas to find missing sides in any triangle given SAS information:
After, we calculate the right side of the equation, we need to take the square root of both sides in order to obtain the final side length of the missing side. Last, we need to use the perimeter formula to obtain the distance of the side lengths of the polygon.
Solution:
Now, that we have discussed the three methods used to calculate the perimeter of a triangle, we can use this information to solve the problem.
First, we need to use the Pythagorean theorem to solve for
Because we are dealing with a triangle, the only valid solution is
After you have found
Compare your answer with the correct one above
Find the perimeter of the triangle below.
Find the perimeter of the triangle below.
How do you find the perimeter of a right triangle?
There are three primary methods used to find the perimeter of a right triangle.
- When side lengths are given, add them together.
- Solve for a missing side using the Pythagorean theorem.
- If we know side-angle-side information, solve for the missing side using the Law of Cosines.
Method 1:
This method will show you how to calculate the perimeter of a triangle when all sides lengths are known. Consider the following figure:
If we know the lengths of sides , , and , then we can simply add them together to find the perimeter of the triangle. It is important to note several things. First, we need to make sure that all the units given match one another. Second, when all the side lengths are known, then the perimeter formula may be used on all types of triangles (e.g. right, acute, obtuse, equilateral, isosceles, and scalene). The perimeter formula is written formally in the following format:
Method 2:
In right triangles, we can calculate the perimeter of a triangle when we are provided only two sides. We can do this by using the Pythagorean theorem. Let's first discuss right triangles in a general sense. A right triangle is a triangle that has one angle. It is a special triangle and needs to be labeled accordingly. The legs of the triangle form the angle and they are labeled and . The side of the triangle that is opposite of the angle and connects the two legs is known as the hypotenuse. The hypotenuse is the longest side of the triangle and is labeled as .
If a triangle appears in this format, then we can use the Pythagorean theorem to solve for any missing side. This formula is written in the following manner:
We can rearrange it in a number of ways to solve for each of the sides of the triangle. Let's rearrange it to solve for the hypotenuse, .
Rearrange and take the square root of both sides.
Simplify.
Now, let's use the Pythagorean theorem to solve for one of the legs, .
Subtract from both sides of the equation.
Take the square root of both sides.
Simplify.
Last, let's use the Pythagorean theorem to solve for the adjacent leg, .
Subtract from both sides of the equation.
Take the square root of both sides.
Simplify.
It is important to note that we can only use the following formulas to solve for the missing side of a right triangle when two other sides are known:
After we find the missing side, we can use the perimeter formula to calculate the triangle's perimeter.
Method 3:
This method is the most complicated method and can only be used when we know two side lengths of a triangle as well as the measure of the angle that is between them. When we know side-angle-side (SAS) information, we can use the Law of Cosines to find the missing side. In order for this formula to accurately calculate the missing side we need to label the triangle in the following manner:
When the triangle is labeled in this way each side directly corresponds to the angle directly opposite of it. If we label our triangle carefully, then we can use the following formulas to find missing sides in any triangle given SAS information:
After, we calculate the right side of the equation, we need to take the square root of both sides in order to obtain the final side length of the missing side. Last, we need to use the perimeter formula to obtain the distance of the side lengths of the polygon.
Solution:
Now, that we have discussed the three methods used to calculate the perimeter of a triangle, we can use this information to solve the problem. The perimeter of a triangle is simply the sum of its three sides. Our problem is that we only know two of the sides. The key for us is the fact that we have a right triangle (as indicated by the little box in the one angle). Knowing two sides of a right triangle and needing the third is a classic case for using the Pythagorean theorem. In simple (sort of), the Pythagorean theorem says that sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of its hypotenuse.
Every right triangle has three sides and a right angle. The side across from the right angle (also the longest) is called the hypotenuse. The other two sides are each called legs. That means in our triangle, the side with length 17 is the hypotenuse, while the one with length 8 and the one we need to find are each legs.
What the Pythagorean theorem tells us is that if we square the lengths of our two legs and add those two numbers together, we get the same number as when we square the length of our hypotenuse. Since we don't know the length of our second leg, we can identify it with the variable 
.
This allows us to create the following algebraic equation:
which simplified becomes
To solve this equation, we first need to get the variable by itself, which can be done by subtracting 64 from both sides, giving us
From here, we simply take the square root of both sides.
Technically, 
would also be a square root of 225, but since a side of a triangle can only have a positive length, we'll stick with 15 as our answer.
But we aren't done yet. We now know the length of our missing side, but we still need to add the three side lengths together to find the perimeter.
Our answer is 40.
How do you find the perimeter of a right triangle?
There are three primary methods used to find the perimeter of a right triangle.
- When side lengths are given, add them together.
- Solve for a missing side using the Pythagorean theorem.
- If we know side-angle-side information, solve for the missing side using the Law of Cosines.
Method 1:
This method will show you how to calculate the perimeter of a triangle when all sides lengths are known. Consider the following figure:
If we know the lengths of sides
Method 2:
In right triangles, we can calculate the perimeter of a triangle when we are provided only two sides. We can do this by using the Pythagorean theorem. Let's first discuss right triangles in a general sense. A right triangle is a triangle that has one
If a triangle appears in this format, then we can use the Pythagorean theorem to solve for any missing side. This formula is written in the following manner:
We can rearrange it in a number of ways to solve for each of the sides of the triangle. Let's rearrange it to solve for the hypotenuse,
Rearrange and take the square root of both sides.
Simplify.
Now, let's use the Pythagorean theorem to solve for one of the legs,
Subtract
Take the square root of both sides.
Simplify.
Last, let's use the Pythagorean theorem to solve for the adjacent leg,
Subtract
Take the square root of both sides.
Simplify.
It is important to note that we can only use the following formulas to solve for the missing side of a right triangle when two other sides are known:
After we find the missing side, we can use the perimeter formula to calculate the triangle's perimeter.
Method 3:
This method is the most complicated method and can only be used when we know two side lengths of a triangle as well as the measure of the angle that is between them. When we know side-angle-side (SAS) information, we can use the Law of Cosines to find the missing side. In order for this formula to accurately calculate the missing side we need to label the triangle in the following manner:
When the triangle is labeled in this way each side directly corresponds to the angle directly opposite of it. If we label our triangle carefully, then we can use the following formulas to find missing sides in any triangle given SAS information:
After, we calculate the right side of the equation, we need to take the square root of both sides in order to obtain the final side length of the missing side. Last, we need to use the perimeter formula to obtain the distance of the side lengths of the polygon.
Solution:
Now, that we have discussed the three methods used to calculate the perimeter of a triangle, we can use this information to solve the problem. The perimeter of a triangle is simply the sum of its three sides. Our problem is that we only know two of the sides. The key for us is the fact that we have a right triangle (as indicated by the little box in the one angle). Knowing two sides of a right triangle and needing the third is a classic case for using the Pythagorean theorem. In simple (sort of), the Pythagorean theorem says that sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of its hypotenuse.
Every right triangle has three sides and a right angle. The side across from the right angle (also the longest) is called the hypotenuse. The other two sides are each called legs. That means in our triangle, the side with length 17 is the hypotenuse, while the one with length 8 and the one we need to find are each legs.
What the Pythagorean theorem tells us is that if we square the lengths of our two legs and add those two numbers together, we get the same number as when we square the length of our hypotenuse. Since we don't know the length of our second leg, we can identify it with the variable
This allows us to create the following algebraic equation:
which simplified becomes
To solve this equation, we first need to get the variable by itself, which can be done by subtracting 64 from both sides, giving us
From here, we simply take the square root of both sides.
Technically,
But we aren't done yet. We now know the length of our missing side, but we still need to add the three side lengths together to find the perimeter.
Our answer is 40.
Compare your answer with the correct one above
Given that two sides of a right triangle are 
and 
and the hypotenuse is unknown, find the perimeter of the triangle.
Given that two sides of a right triangle are
How do you find the perimeter of a right triangle?
There are three primary methods used to find the perimeter of a right triangle.
- When side lengths are given, add them together.
- Solve for a missing side using the Pythagorean theorem.
- If we know side-angle-side information, solve for the missing side using the Law of Cosines.
Method 1:
This method will show you how to calculate the perimeter of a triangle when all sides lengths are known. Consider the following figure:
If we know the lengths of sides , , and , then we can simply add them together to find the perimeter of the triangle. It is important to note several things. First, we need to make sure that all the units given match one another. Second, when all the side lengths are known, then the perimeter formula may be used on all types of triangles (e.g. right, acute, obtuse, equilateral, isosceles, and scalene). The perimeter formula is written formally in the following format:
Method 2:
In right triangles, we can calculate the perimeter of a triangle when we are provided only two sides. We can do this by using the Pythagorean theorem. Let's first discuss right triangles in a general sense. A right triangle is a triangle that has one angle. It is a special triangle and needs to be labeled accordingly. The legs of the triangle form the angle and they are labeled and . The side of the triangle that is opposite of the angle and connects the two legs is known as the hypotenuse. The hypotenuse is the longest side of the triangle and is labeled as .
If a triangle appears in this format, then we can use the Pythagorean theorem to solve for any missing side. This formula is written in the following manner:
We can rearrange it in a number of ways to solve for each of the sides of the triangle. Let's rearrange it to solve for the hypotenuse, .
Rearrange and take the square root of both sides.
Simplify.
Now, let's use the Pythagorean theorem to solve for one of the legs, .
Subtract from both sides of the equation.
Take the square root of both sides.
Simplify.
Last, let's use the Pythagorean theorem to solve for the adjacent leg, .
Subtract from both sides of the equation.
Take the square root of both sides.
Simplify.
It is important to note that we can only use the following formulas to solve for the missing side of a right triangle when two other sides are known:
After we find the missing side, we can use the perimeter formula to calculate the triangle's perimeter.
Method 3:
This method is the most complicated method and can only be used when we know two side lengths of a triangle as well as the measure of the angle that is between them. When we know side-angle-side (SAS) information, we can use the Law of Cosines to find the missing side. In order for this formula to accurately calculate the missing side we need to label the triangle in the following manner:
When the triangle is labeled in this way each side directly corresponds to the angle directly opposite of it. If we label our triangle carefully, then we can use the following formulas to find missing sides in any triangle given SAS information:
After, we calculate the right side of the equation, we need to take the square root of both sides in order to obtain the final side length of the missing side. Last, we need to use the perimeter formula to obtain the distance of the side lengths of the polygon.
Solution:
Now, that we have discussed the three methods used to calculate the perimeter of a triangle, we can use this information to solve the problem.
In order to calculate the perimeter we need to find the length of the hypotenuse using the Pythagorean theorem.
Rearrange.
Substitute in known values.
Now that we have found the missing side, we can substitute the values into the perimeter formula and solve.
How do you find the perimeter of a right triangle?
There are three primary methods used to find the perimeter of a right triangle.
- When side lengths are given, add them together.
- Solve for a missing side using the Pythagorean theorem.
- If we know side-angle-side information, solve for the missing side using the Law of Cosines.
Method 1:
This method will show you how to calculate the perimeter of a triangle when all sides lengths are known. Consider the following figure:
If we know the lengths of sides
Method 2:
In right triangles, we can calculate the perimeter of a triangle when we are provided only two sides. We can do this by using the Pythagorean theorem. Let's first discuss right triangles in a general sense. A right triangle is a triangle that has one
If a triangle appears in this format, then we can use the Pythagorean theorem to solve for any missing side. This formula is written in the following manner:
We can rearrange it in a number of ways to solve for each of the sides of the triangle. Let's rearrange it to solve for the hypotenuse,
Rearrange and take the square root of both sides.
Simplify.
Now, let's use the Pythagorean theorem to solve for one of the legs,
Subtract
Take the square root of both sides.
Simplify.
Last, let's use the Pythagorean theorem to solve for the adjacent leg,
Subtract
Take the square root of both sides.
Simplify.
It is important to note that we can only use the following formulas to solve for the missing side of a right triangle when two other sides are known:
After we find the missing side, we can use the perimeter formula to calculate the triangle's perimeter.
Method 3:
This method is the most complicated method and can only be used when we know two side lengths of a triangle as well as the measure of the angle that is between them. When we know side-angle-side (SAS) information, we can use the Law of Cosines to find the missing side. In order for this formula to accurately calculate the missing side we need to label the triangle in the following manner:
When the triangle is labeled in this way each side directly corresponds to the angle directly opposite of it. If we label our triangle carefully, then we can use the following formulas to find missing sides in any triangle given SAS information:
After, we calculate the right side of the equation, we need to take the square root of both sides in order to obtain the final side length of the missing side. Last, we need to use the perimeter formula to obtain the distance of the side lengths of the polygon.
Solution:
Now, that we have discussed the three methods used to calculate the perimeter of a triangle, we can use this information to solve the problem.
In order to calculate the perimeter we need to find the length of the hypotenuse using the Pythagorean theorem.
Rearrange.
Substitute in known values.
Now that we have found the missing side, we can substitute the values into the perimeter formula and solve.
Compare your answer with the correct one above
The ratio for the side lengths of a right triangle is 3:4:5. If the perimeter is 48, what is the area of the triangle?
The ratio for the side lengths of a right triangle is 3:4:5. If the perimeter is 48, what is the area of the triangle?
We can model the side lengths of the triangle as 3x, 4x, and 5x. We know that perimeter is 3x+4x+5x=48, which implies that x=4. This tells us that the legs of the right triangle are 3x=12 and 4x=16, therefore the area is A=1/2 bh=(1/2)(12)(16)=96.
We can model the side lengths of the triangle as 3x, 4x, and 5x. We know that perimeter is 3x+4x+5x=48, which implies that x=4. This tells us that the legs of the right triangle are 3x=12 and 4x=16, therefore the area is A=1/2 bh=(1/2)(12)(16)=96.
Compare your answer with the correct one above
A right triangle has a total perimeter of 12, and the length of its hypotenuse is 5. What is the area of this triangle?
A right triangle has a total perimeter of 12, and the length of its hypotenuse is 5. What is the area of this triangle?
The area of a triangle is denoted by the equation 1/2 b x h.
b stands for the length of the base, and h stands for the height.
Here we are told that the perimeter (total length of all three sides) is 12, and the hypotenuse (the side that is neither the height nor the base) is 5 units long.
So, 12-5 = 7 for the total perimeter of the base and height.
7 does not divide cleanly by two, but it does break down into 3 and 4,
and 1/2 (3x4) yields 6.
Another way to solve this would be if you recall your rules for right triangles, one of the very basic ones is the 3,4,5 triangle, which is exactly what we have here
The area of a triangle is denoted by the equation 1/2 b x h.
b stands for the length of the base, and h stands for the height.
Here we are told that the perimeter (total length of all three sides) is 12, and the hypotenuse (the side that is neither the height nor the base) is 5 units long.
So, 12-5 = 7 for the total perimeter of the base and height.
7 does not divide cleanly by two, but it does break down into 3 and 4,
and 1/2 (3x4) yields 6.
Another way to solve this would be if you recall your rules for right triangles, one of the very basic ones is the 3,4,5 triangle, which is exactly what we have here
Compare your answer with the correct one above
The length of one leg of an equilateral triangle is 6. What is the area of the triangle?
The length of one leg of an equilateral triangle is 6. What is the area of the triangle?
The base is equal to 6.
The height of an quilateral triangle is equal to 
, where 
is the length of the base.
The base is equal to 6.
The height of an quilateral triangle is equal to
Compare your answer with the correct one above
Find the area of the following right triangle to the nearest integer 
Note: The triangle is not necessarily to scale
Find the area of the following right triangle to the nearest integer
Note: The triangle is not necessarily to scale
The equation used to find the area of a right triangle is: 
where A is the area, b is the base, and h is the height of the triangle. In this question, we are given the height, so we need to figure out the base in order to find the area. Since we know both the height and hypotenuse of the triangle, the quickest way to finding the base is using the pythagorean theorem, 
. a = the height, b = the base, and c = the hypotenuse.
Using the given information, we can write 
. Solving for b, we get 
or 
. Now that we have both the base and height, we can solve the original equation for the area of the triangle. 
The equation used to find the area of a right triangle is:
Using the given information, we can write
Compare your answer with the correct one above
In the above triangle, if 
and 
what is the area of the triangle?
In the above triangle, if
To find the area of a triangle use the formula:
, since the base is 
and the height is 
, plugging in yields:
To find the area of a triangle use the formula:
Compare your answer with the correct one above
A right triangle has integer sides with a ratio of 
, measured in 
. What is the smallest possible area of this triangle?
A right triangle has integer sides with a ratio of
The easiest way to find the smallest possible integer sides is to simply factor the ratio we are given. In this case, 
is already prime (since 
is a prime number), so the smallest possible sides which hold to this triangle are 
and 
. You may also recognize this number as a common Pythagorean triple.
The area of a triangle is expressed as 
, where 
is the length and 
is the height. Since our triangle is right, we know that two lines intersect at a 
angle and thus serve well as our length and height. We also know that the longest side is always the hypotenuse, so the other two sides must be 
and 
.
Applying our formula, we get:
Thus, the smallest possible area for our triangle is 
.
The easiest way to find the smallest possible integer sides is to simply factor the ratio we are given. In this case,
The area of a triangle is expressed as
Applying our formula, we get:
Thus, the smallest possible area for our triangle is
Compare your answer with the correct one above
Right triangle 
has hypotenuse 
cm and 
. Find the area of the triangle, in cm2, by using 
.
Round angles to four significant figures. Round side lengths to the nearest integer.
Right triangle
Round angles to four significant figures. Round side lengths to the nearest integer.
To find the area of a right triangle, find the lengths of the two perpendicular legs (since this gives us our length and height for the area formula).
In this case, we know that one angle is 
, and SOHCAHTOA tells us that 
, so:
Substitute the angle measure and hypotenuse into the formula.
Isolate the variable.
Solve the left side (rounding to the nearest integer) using our Pythagorean formula:
---> 
Substitute known values.
---> Simplify.
Square root both sides.
So with our two legs solved for, we now only need to apply the area formula for triangles to get our answer:
So, the area of our triangle is 
.
To find the area of a right triangle, find the lengths of the two perpendicular legs (since this gives us our length and height for the area formula).
In this case, we know that one angle is
So with our two legs solved for, we now only need to apply the area formula for triangles to get our answer:
So, the area of our triangle is
Compare your answer with the correct one above
Find the area of a right triangle whose height is 4 and base is 5.
Find the area of a right triangle whose height is 4 and base is 5.
To solve, simply use the formula for the area of a triangle given height h and base B.
Substitute
and 
into the area formula.
Thus,
To solve, simply use the formula for the area of a triangle given height h and base B.
Substitute
Thus,
Compare your answer with the correct one above
A right triangle is defined by the points (1, 1), (1, 5), and (4, 1). The triangle's sides are enlarged by a factor of 3 to form a new triangle. What is the area of the new triangle?
A right triangle is defined by the points (1, 1), (1, 5), and (4, 1). The triangle's sides are enlarged by a factor of 3 to form a new triangle. What is the area of the new triangle?
The points define a 3-4-5 right triangle. Its area is A = 1/2bh = ½(3)(4) = 6. The scale factor (SF) of the new triangle is 3. The area of the new triangle is given by Anew = (SF)2 x (Aold) =
32 x 6 = 9 x 6 = 54 square units (since the units are not given in the original problem).
NOTE: For a volume problem: Vnew = (SF)3 x (Vold).
The points define a 3-4-5 right triangle. Its area is A = 1/2bh = ½(3)(4) = 6. The scale factor (SF) of the new triangle is 3. The area of the new triangle is given by Anew = (SF)2 x (Aold) =
32 x 6 = 9 x 6 = 54 square units (since the units are not given in the original problem).
NOTE: For a volume problem: Vnew = (SF)3 x (Vold).
Compare your answer with the correct one above
You have two right triangles that are similar. The base of the first is 6 and the height is 9. If the base of the second triangle is 20, what is the height of the second triangle?
You have two right triangles that are similar. The base of the first is 6 and the height is 9. If the base of the second triangle is 20, what is the height of the second triangle?
Similar triangles are proportional.
Base1 / Height1 = Base2 / Height2
6 / 9 = 20 / Height2
Cross multiply and solve for Height2
6 / 9 = 20 / Height2
6 * Height2= 20 * 9
Height2= 30
Similar triangles are proportional.
Base1 / Height1 = Base2 / Height2
6 / 9 = 20 / Height2
Cross multiply and solve for Height2
6 / 9 = 20 / Height2
6 * Height2= 20 * 9
Height2= 30
Compare your answer with the correct one above
On a flat street, a light pole 36 feet tall casts a shadow that is 9 feet long. At the same time of day, a nearby light pole casts a shadow that is 6 feet long. How many feet tall is the second light pole?
On a flat street, a light pole 36 feet tall casts a shadow that is 9 feet long. At the same time of day, a nearby light pole casts a shadow that is 6 feet long. How many feet tall is the second light pole?
Start by drawing out the light poles and their shadows.
In this case, we end up with two similar triangles. We know that these are similar triangles because the question tells us that these poles are on a flat surface, meaning angle B and angle E are both right angles. Then, because the question states that the shadow cast by both poles are at the same time of day, we know that angles C and F are equivalent. As a result, angles A and D must also be equivalent.
Since these are similar triangles, we can set up proportions for the corresponding sides.
Now, solve for 
by cross-multiplying.
Start by drawing out the light poles and their shadows.
In this case, we end up with two similar triangles. We know that these are similar triangles because the question tells us that these poles are on a flat surface, meaning angle B and angle E are both right angles. Then, because the question states that the shadow cast by both poles are at the same time of day, we know that angles C and F are equivalent. As a result, angles A and D must also be equivalent.
Since these are similar triangles, we can set up proportions for the corresponding sides.
Now, solve for
Compare your answer with the correct one above
In a right triangle ABC, the measure of angle C is greater than 60 degrees. Which of the following statements could describe the measures of angles A and B?
In a right triangle ABC, the measure of angle C is greater than 60 degrees. Which of the following statements could describe the measures of angles A and B?
Given that it is a right triangle, either angle A or B has to be 90 degrees. The other angle then must be less than 30 degrees, given that C is greater than 60 because there are 180 degrees in a triangle.
Example:
If angle C is 61 degrees and angle A is 90 degrees, then angle B must be 29 degrees in order for the angle measures to sum to 180 degrees.
Given that it is a right triangle, either angle A or B has to be 90 degrees. The other angle then must be less than 30 degrees, given that C is greater than 60 because there are 180 degrees in a triangle.
Example:
If angle C is 61 degrees and angle A is 90 degrees, then angle B must be 29 degrees in order for the angle measures to sum to 180 degrees.
Compare your answer with the correct one above
A 17 ft ladder is propped against a 15 ft wall. What is the degree measurement between the ladder and the ground?
A 17 ft ladder is propped against a 15 ft wall. What is the degree measurement between the ladder and the ground?
Since all the answer choices are in trigonometric form, we know we must not necessarily solve for the exact value (although we can do that and calculate each choice to see if it matches). The first step is to determine the length of the ground between the bottom of the ladder and the wall via the Pythagorean Theorem: "x2 + 152 = 172"; x = 8. Using trigonometric definitions, we know that "opposite/adjecent = tan(theta)"; since we have both values of the sides (opp = 15 and adj = 8), we can plug into the tangential form tan(theta) = 15/8. However, since we are solving for theta, we must take the inverse tangent of the left side, "tan-1". Thus, our final answer is
Since all the answer choices are in trigonometric form, we know we must not necessarily solve for the exact value (although we can do that and calculate each choice to see if it matches). The first step is to determine the length of the ground between the bottom of the ladder and the wall via the Pythagorean Theorem: "x2 + 152 = 172"; x = 8. Using trigonometric definitions, we know that "opposite/adjecent = tan(theta)"; since we have both values of the sides (opp = 15 and adj = 8), we can plug into the tangential form tan(theta) = 15/8. However, since we are solving for theta, we must take the inverse tangent of the left side, "tan-1". Thus, our final answer is
Compare your answer with the correct one above
What is the sine of the angle between the base and the hypotenuse of a right triangle with a base of 4 and a height of 3?
What is the sine of the angle between the base and the hypotenuse of a right triangle with a base of 4 and a height of 3?
By rule, this is a 3-4-5 right triangle. Sine = (the opposite leg)/(the hypotenuse). This gives us 3/5.
By rule, this is a 3-4-5 right triangle. Sine = (the opposite leg)/(the hypotenuse). This gives us 3/5.
Compare your answer with the correct one above
The measure of 3 angles in a triangle are in a 1:2:3 ratio. What is the measure of the middle angle?
The measure of 3 angles in a triangle are in a 1:2:3 ratio. What is the measure of the middle angle?
The angles in a triangle sum to 180 degrees. This makes the middle angle 60 degrees.
The angles in a triangle sum to 180 degrees. This makes the middle angle 60 degrees.
Compare your answer with the correct one above
Right triangle 
has an acute angle measuring 
. What is the measure of the other acute angle?
Right triangle
The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle must be 
. We know that a right triangle has one angle equal to 
, and we are told one of the acute angles is 
.
The rest is simple subtraction:
Thus, our missing angle is 
.
The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle must be
The rest is simple subtraction:
Thus, our missing angle is
Compare your answer with the correct one above
Right triangle 
has angles with a ratio of with a ratio of 
. What is the smallest angle in the triangle?
Right triangle
Solving this problem quickly requires that we recognize how to break apart our ratio.
The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle is 
. Additionally, the Right Triangle Acute Angle Theorem states that the two non-right angles in a right triangle are acute; that is to say, the right angle is always the largest angle in a right triangle.
Since this is true, we can assume that 
is represented by the largest number in the ratio of angles. Now consider that the other two angles must also sum to 
. We know therefore that the sum of their ratios must be divisible by 
as well.
Thus, 
.
To find the value of one angle of the ratio, simply assign fractional value to the sum of the ratios and multiply by 
.
, so:
Thus, the shortest angle (the one represented by 
in our ratio of angles) is 
.
Solving this problem quickly requires that we recognize how to break apart our ratio.
The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle is
Since this is true, we can assume that
Thus,
To find the value of one angle of the ratio, simply assign fractional value to the sum of the ratios and multiply by
Thus, the shortest angle (the one represented by
Compare your answer with the correct one above