# SSAT Upper Level Math : How to find the length of the side of a right triangle

## Example Questions

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### Example Question #1 : Right Triangles

A right triangle has a hypotenuse of 39 and one leg is 36. What is the length of the other leg?

Explanation:

You may recognize these numbers as multiples of 13 and 12 (each by a factor of 3) and remember that sides of length 5, 12 and 13 make a special right triangle. So the other leg would be 15 .

If you don't remember this, you can use Pythagorean theorem:

### Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has a hypotenuse of  and one leg has a length of . What is the length of the other leg?

Explanation:

When calculating the lengths of sides of a right triangle, we can use the Pythagorean Theorem as follows:

, where  and  are legs of the triangle and  is the hypotenuse.

Plugging in our given values:

Subtracting  from each side of the equation:

Taking the square root of each side of the equation:

Simplifying the square root:

### Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has two legs of length  and , respectively. What is the hypotenuse of the right triangle?

Explanation:

When calculating the lengths of sides of a right triangle, we can use the Pythagorean Theorem as follows:

, where  and  are legs of the triangle and  is the hypotenuse.

Plugging in our given values:

### Example Question #4 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has a leg of length  and a hypotenuse of length . What is the length of the other leg?

Explanation:

When calculating the lengths of sides of a right triangle, we can use the Pythagorean Theorem as follows:

, where  and  are legs of the triangle and  is the hypotenuse.

Plugging in our given values:

Subtracting  from each side of the equation:

### Example Question #5 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

### Example Question #6 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

### Example Question #7 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

### Example Question #8 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

### Example Question #9 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.

Explanation:

Use the Pythagorean Theorem to find the length of the missing side.

### Example Question #10 : How To Find The Length Of The Side Of A Right Triangle

Find the length of the missing side.