How to find the height of a triangle with only the base

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

Correct answer:

Explanation:

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.

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

Possible Answers:

None of the other answers

 or 

Correct answer:

 or 

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

Correct answer:

Explanation:

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

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

We can then solve by simply dividing.

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

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

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

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

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

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

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

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

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

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

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

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

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

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

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

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

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

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

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

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

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

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

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

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

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

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

Correct answer:

Explanation:

Recall how to find the area of a right triangle:

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

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

All Basic Geometry Resources

What is the formula for height of a triangle?