Isosceles Triangles - Math
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An isoceles triangle has a vertex angle that is twenty more than twice the base angle. What is the difference between the vertex and base angles?
An isoceles triangle has a vertex angle that is twenty more than twice the base angle. What is the difference between the vertex and base angles?
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A triangle has 
degrees. An isoceles triangle has one vertex angle and two congruent base angles.
Let 
= the base angle and 
= vertex angle
So the equation to solve becomes 
or
so the base angle is 
and the vertex angle is 
and the difference is 
.
A triangle has
Let
So the equation to solve becomes
or
so the base angle is
An ssosceles triangle has interior angles of 
degrees and 
degrees. Find the missing angle.
An ssosceles triangle has interior angles of
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
The largest angle in an obtuse isosceles triangle is 
degrees. Find the measurement of one of the two equivalent interior angles.
The largest angle in an obtuse isosceles triangle is
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
The two equivalent interior angles of an obtuse isosceles triangle each have a measurement of 
degrees. Find the measurement of the obtuse angle.
The two equivalent interior angles of an obtuse isosceles triangle each have a measurement of
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of 
degrees.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
In an obtuse isosceles triangle the angle measurements are, 
, 
, and 
. Find the measurement of one of the acute angles.
In an obtuse isosceles triangle the angle measurements are,
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
However, 
degrees is the measurement of both of the acute angles combined.
Each individual angle is 
.
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
However,
Each individual angle is
In an acute isosceles triangle the two equivalent interior angles each have a measurement of 
degrees. Find the missing angle.
In an acute isosceles triangle the two equivalent interior angles each have a measurement of
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
In an acute isosceles triangle the two equivalent interior angles are each 
degrees. Find the missing angle.
In an acute isosceles triangle the two equivalent interior angles are each
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
The largest angle in an obtuse isosceles triangle is 
degrees. Find the measurement of one of the equivalent interior angles.
The largest angle in an obtuse isosceles triangle is
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse Isosceles triangle, the two missing angles must be acute angles.
Thus, the solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
Thus, the solution is:
In an obtuse isosceles triangle the largest angle is 
degrees. Find the measurement of one of the acute angles.
In an obtuse isosceles triangle the largest angle is
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
In an acute isosceles triangle the measurement of the non-equivalent interior angle is 
degrees. Find the measurement of one of the equivalent interior angles.
In an acute isosceles triangle the measurement of the non-equivalent interior angle is
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an acute isosceles triangle, all of the interior angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
In an obtuse isosceles triangle, the largest interior angle is 
degrees. What is the measurement of one of the equivalent interior angles?
In an obtuse isosceles triangle, the largest interior angle is
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Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees. Since this is an obtuse isosceles triangle, the two missing angles must be acute angles.
The solution is:
Isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of
The solution is:
You are flying a kite at an altitude of 40 feet after having let out 75 feet of string. What is the kite's angle of elevation from where you are holding the spool of string at a height of 4 feet off the ground? Round answer to one decimal place.
You are flying a kite at an altitude of 40 feet after having let out 75 feet of string. What is the kite's angle of elevation from where you are holding the spool of string at a height of 4 feet off the ground? Round answer to one decimal place.
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First, we must draw a picture to include all important parts given in the problem.
Once this is determined we can use trigonometry to find the angle of elevation.
Use the inverse sin on a calculator to solve.
First, we must draw a picture to include all important parts given in the problem.
Once this is determined we can use trigonometry to find the angle of elevation.
Use the inverse sin on a calculator to solve.
Two angles in an isosceles triangle are 50 and 80 degrees respectively. What is the measure of the third angle?
Two angles in an isosceles triangle are 50 and 80 degrees respectively. What is the measure of the third angle?
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If a triangle is isosceles, two of the angles must be congruent. So the angle must be either 50 degrees or 80 degrees.
We know that the three angles in all triangles must sum to equal 180 degrees. The only answer choice that is both the same as one of the given angles and results in a sum equal to 180 degrees is the 50 degree angle.
50+50+80=180.
If a triangle is isosceles, two of the angles must be congruent. So the angle must be either 50 degrees or 80 degrees.
We know that the three angles in all triangles must sum to equal 180 degrees. The only answer choice that is both the same as one of the given angles and results in a sum equal to 180 degrees is the 50 degree angle.
50+50+80=180.
An isosceles triangle has one angle measuring 
. Which of the following are possible values for angles in this triangle?
An isosceles triangle has one angle measuring
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An isosceles triangle has 2 congruent angles and then a third angle. These angles, as in any triangle, must add to 180.
One possibility is that the 25-degree angle is the "different" one, and the other two are congruent. This could be expressed using the algebraic expression 
. To find the other two angles, solve for x. First combine like terms:
subtract 25 from both sides
divide both sides by 2
The other possibility is that there are 2 25-degree angles and then some different angle measure. This could be expressed using the algebraic expression 
. Again, solve for x. First add the 2 25's to get 50:
subtract 50 from both sides
An isosceles triangle has 2 congruent angles and then a third angle. These angles, as in any triangle, must add to 180.
One possibility is that the 25-degree angle is the "different" one, and the other two are congruent. This could be expressed using the algebraic expression
The other possibility is that there are 2 25-degree angles and then some different angle measure. This could be expressed using the algebraic expression
Refer to the above triangle. By what statement does it follow that 
?
Refer to the above triangle. By what statement does it follow that
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We are given that, in 
, two sides are congruent; specifically, 
. It is a consequence of the Isosceles Triangle Theorem that the angles opposite the sides are also congruent - that is, 
.
We are given that, in
An isosceles triangle has a base of 12 cm and an area of 42 $cm^{2}$. What must be the height of this triangle?
An isosceles triangle has a base of 12 cm and an area of 42 $cm^{2}$. What must be the height of this triangle?
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A=\frac{1}{2}$bh.
6x=42
x=7
A=\frac{1}{2}$bh.
6x=42
x=7
An isosceles triangle has a perimeter of 
. If the base of the triangle is two less than two times the length of each leg, what is the height of the triangle?
An isosceles triangle has a perimeter of
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First, find the lengths of the triangle.
Let 
be the length of each leg. Then, the length of the base must be 
.
Use the information given about the perimeter to solve for 
.
Plug this value in to find the length of the base.
Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.
Thus, we can use the Pythagorean Theorem to find the length of the height.
Plug in the given values to find the height of the triangle.
Make sure to round to 
places after the decimal.
First, find the lengths of the triangle.
Let
Use the information given about the perimeter to solve for
Plug this value in to find the length of the base.
Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.
Thus, we can use the Pythagorean Theorem to find the length of the height.
Plug in the given values to find the height of the triangle.
Make sure to round to
An isosceles triangle has a perimeter of 
. If the base of the triangle is 
less than three times the length of a leg, what is the height of the triangle?
An isosceles triangle has a perimeter of
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First, find the lengths of the triangle.
Let 
be the length of each leg. Then, the length of the base must be 
.
Use the information given about the perimeter to solve for 
.
Plug this value in to find the length of the base.
Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.
Thus, we can use the Pythagorean Theorem to find the length of the height.
Plug in the given values to find the height of the triangle.
Make sure to round to 
places after the decimal.
First, find the lengths of the triangle.
Let
Use the information given about the perimeter to solve for
Plug this value in to find the length of the base.
Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.
Thus, we can use the Pythagorean Theorem to find the length of the height.
Plug in the given values to find the height of the triangle.
Make sure to round to
An isosceles triangle has a perimeter of 
. If the length of the base is one less than twice the length of a leg, what is the height of the triangle?
An isosceles triangle has a perimeter of
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First, find the lengths of the triangle.
Let 
be the length of each leg. Then, the length of the base must be 
.
Use the information given about the perimeter to solve for 
.
Plug this value in to find the length of the base.
Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.
Thus, we can use the Pythagorean Theorem to find the length of the height.
Plug in the given values to find the height of the triangle.
Make sure to round to 
places after the decimal.
First, find the lengths of the triangle.
Let
Use the information given about the perimeter to solve for
Plug this value in to find the length of the base.
Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.
Thus, we can use the Pythagorean Theorem to find the length of the height.
Plug in the given values to find the height of the triangle.
Make sure to round to
An isosceles triangle has a perimeter of 
. If the length of the base is fourteen less than three times the length of a leg, what is the height of the triangle?
An isosceles triangle has a perimeter of
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First, find the lengths of the triangle.
Let 
be the length of each leg. Then, the length of the base must be 
.
Use the information given about the perimeter to solve for 
.
Plug this value in to find the length of the base.
Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.
Thus, we can use the Pythagorean Theorem to find the length of the height.
Plug in the given values to find the height of the triangle.
Make sure to round to 
places after the decimal.
First, find the lengths of the triangle.
Let
Use the information given about the perimeter to solve for
Plug this value in to find the length of the base.
Now, recall that the height of an isosceles triangle can split the entire triangle into two congruent right triangle as shown by the figure below.
Thus, we can use the Pythagorean Theorem to find the length of the height.
Plug in the given values to find the height of the triangle.
Make sure to round to