ACT Math : Right Triangles
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Example Questions
Example Question #63 : Triangles
The lengths of the sides of a right triangle are consecutive integers, and the length of the shortest side is 
Since the lengths of the sides are consecutive integers and the shortest side is 
We then use the Pythagorean Theorem:
Example Question #114 : Geometry
Square 
Quantity A:
Quantity B: The distance between points 
The relationship cannot be determined from the information provided.
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
The two quantities are equal.
To find the distance between points 
Example Question #124 : Geometry
What is the diagonal of a computer screen that measures 
Plug the values into the Pythagorean Theorem
because we are solving for the diagonal we are looking for 
Example Question #131 : Geometry
A right triangle has legs of length 
To find the hypotenuse of a right triangle, use the Pythagorean Theorem and plug the leg values in for 
Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem
A right triangle has a base of six and a height of eight. Using this information find the hypotenuse.
This question calls for us to use the Pythagorean Theorem. This theorem has a formula of
where a and b are the sides of a right triangle, adjacent to the right angle, and c is the hypotenuse.
Given our information
Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem
A right triangle has a base of seven and a height of twelve. Using this information find the hypotenuse.
This question calls for us to use the Pythagorean Theorem. This theorem has a formula of
where a and b are the sides of a right triangle, adjacent to the right angle, and c is the hypotenuse.
Given our information
Example Question #132 : Geometry
Marcus Absent is marking out some lines for a large canvas tent. He paces out 
How many 
The Pythagorean Theorem states that for any right triangle with legs 
Applying this to Marcus's steps, we know that 
Expand:
So, 
So, Marcus travels exactly 
Example Question #194 : Plane Geometry
Justin travels 
This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that 
Example Question #195 : Plane Geometry
Susie walks north from her house to a park that is 30 meters away. Once she arrives at the park, she turns and walks west for 80 meters to a bench to feed some pigeons. She then walks north for another 30 meters to a concession stand. If Susie returns home in a straight line from the concession stand, how far will she walk from the concession stand to her house, in meters?
200
50
25
100
70
100
Susie walks 30 meters north, then 80 meters west, then 30 meters north again. Thus, she walks 60 meters north and 80 meters west. These two directions are 90 degrees away from one another.
At this point, construct a right triangle with one leg that measures 60 meters and a second leg that is 80 meters.
You can save time by using the 3:4:5 common triangle. 60 and 80 are 
We can solve for the length of the missing hypotenuse by applying the Pythagorean theorem:
Substitute the following known values into the formula and solve for the missing hypotenuse: side 
Susie will walk 100 meters to reach her house.
Example Question #132 : Act Math
The lengths of the sides of a triangle are consecutive odd numbers and the triangle's perimeter is 57 centimeters. What is the length, in centimeters, of its longest side?
17
21
25
19
23
21
First, define the sides of the triangle. Because the side lengths are consecutive odd numbers, if we define the shortest side will be as 
Substitute in the known values and variables.
Subtract 6 from both sides of the equation.
Divide both sides of the equation by 3.
Solve.
This is not the answer; we need to find the length of the longest side, or 
Substitute in the calculated value for 
The longest side of the triangle is 21 centimeters long.
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