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

## Example Questions

### Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has a hypotenuse of 10 and a side of 6. What is the missing side?

Explanation:

To find the missing side, use the Pythagorean Theorem . Plug in (remember c is always the hypotenuse!) so that . Simplify and you get Subtract 36 from both sides so that you get Take the square root of both sides. B is 8.

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

Refer to the above diagram. Which of the following quadratic equations would yield the value of  as a solution?

Explanation:

By the Pythagorean Theorem,

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

Note: Figure NOT drawn to scale.

Refer to the above diagram. Which of the following quadratic equations would yield the value of  as a solution?

Explanation:

By the Pythagorean Theorem,

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

Note: Figure NOT drawn to scale.

Refer to the above diagram.

Find the length of .

Explanation:

First, find .

Since  is an altitude of right  to its hypotenuse,

by the Angle-Angle Postulate, so

### Example Question #51 : Geometry

Note: Figure NOT drawn to scale.

Refer to the above diagram.

Find the length of .

Explanation:

First, find .

Since  is an altitude of  from its right angle to its hypotenuse,

by the Angle-Angle Postulate, so

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

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Explanation:

By the Pythagorean Theorem,

### Example Question #7 : Right Triangles

A right triangle  with hypotenuse  is inscribed in , a circle with radius 26. If , evaluate the length of .

Insufficient information is given to answer the question.