How to find the height of a right triangle - Geometry

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Question

Find the missing length in triangle ABC.

Answer

To find the missing length, use the Pythagorean Theorem.

Where "a" and "b" are the legs, and "c" is the hypotenuse.

a=3 inches

b=???

c= 5 inches

Plug in the values

Now, get the variable by itself.

Take the square root of both sides.

$\sqrt{b^2}=\sqrt{16}$

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Question

A right triangle has a hypotenuse of 18 inches and a base of 12 inches. What is the height of the triangle in inches?

Answer

We can find one leg of a right triangle when we have the length of the hypotenuse and the other leg. Square the hypotenuse and the known leg. Then, subtract the squared length of the leg from the squared length of the hypotenuse. Finally, find the square root of the result.

$\sqrt{18^{2}-12^{2}}=13.42$

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Question

If c is not the base of the triangle, which of the following is the height?

Answer

If is not the base, that makes either or the base. If either or is the base, the right angle is on the bottom, so or respectively will be perpendicular. The height of a triangle is the distance from the base to the highest point, and in a right triangle that will be found by the side adjoining the base at a right angle. So if the base is , then and vise versa.

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Question

The area of a right triangle is 28. If one leg has a length of 7, what is the length of the other leg?

Answer

We begin with the formula for the area of a triangle.

$A=\frac{1}{2}bh$

We further realize that the two legs of the triangle are the base and height; therefore, substituting what we know we get

$28=\frac{1}{2}(7)h$

$28=\frac{7}{2}h$

We can then solve by simply dividing.

We have found our height and thus the second leg of our triangle.

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Question

If the area of a right triangle is , and the base of the right triangle is , what is the height of the right triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(16)}{4}=\frac{32}{4}=8$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(10)}{5}=\frac{20}{5}=4$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(15)}{10}=\frac{30}{10}=3$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(24)}{4}=\frac{48}{4}=12$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(45)}{10}=\frac{90}{10}=9$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(20)}{1}=\frac{40}{1}=40$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(3)}{3}=\frac{6}{3}=2$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(4)}{8}=\frac{8}{8}=1$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(22)}{11}=\frac{44}{11}=4$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(18)}{2}=\frac{36}{2}=18$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(30)}{4}=\frac{60}{4}=15$

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Question

If the area of a right triangle is , and the base of the triangle is , what is the height of the triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(60)}{40}=\frac{120}{40}=3$

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Question

A right triangle has a hypotenuse of 18 inches and a base of 12 inches. What is the height of the triangle in inches?

Answer

We can find one leg of a right triangle when we have the length of the hypotenuse and the other leg. Square the hypotenuse and the known leg. Then, subtract the squared length of the leg from the squared length of the hypotenuse. Finally, find the square root of the result.

$\sqrt{18^{2}-12^{2}}=13.42$

Compare your answer with the correct one above

Question

If c is not the base of the triangle, which of the following is the height?

Answer

If is not the base, that makes either or the base. If either or is the base, the right angle is on the bottom, so or respectively will be perpendicular. The height of a triangle is the distance from the base to the highest point, and in a right triangle that will be found by the side adjoining the base at a right angle. So if the base is , then and vise versa.

Compare your answer with the correct one above

Question

The area of a right triangle is 28. If one leg has a length of 7, what is the length of the other leg?

Answer

We begin with the formula for the area of a triangle.

$A=\frac{1}{2}bh$

We further realize that the two legs of the triangle are the base and height; therefore, substituting what we know we get

$28=\frac{1}{2}(7)h$

$28=\frac{7}{2}h$

We can then solve by simply dividing.

We have found our height and thus the second leg of our triangle.

Compare your answer with the correct one above

Question

If the area of a right triangle is , and the base of the right triangle is , what is the height of the right triangle?

Answer

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(16)}{4}=\frac{32}{4}=8$

Compare your answer with the correct one above

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