# High School Math : How to find the length of the side of a right triangle

## Example Questions

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

A right triangle with a base of 12 and hypotenuse of 15 is shown below. Find x.

4.5

3.5

4

5

5.5

4

Explanation:

Using the Pythagorean Theorem, the height of the right triangle is found to be = √(〖15〗–〖12〗2) = 9, so x=9 – 5=4

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

A right triangle has sides of 36 and 39(hypotenuse).  Find the length of the third side

42

15

33

33√2

12 √6

15

Explanation:

use the pythagorean theorem:

a2 + b2 = c2  ; a and b are sides, c is the hypotenuse

a2 + 1296 = 1521

a2 = 225

a = 15

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

Bob the Helicopter is at 30,000 ft. above sea level, and as viewed on a map his airport is 40,000 ft. away. If Bob travels in a straight line to his airport at 250 feet per second, how many minutes will it take him to arrive?

2 hours and 30 minutes

3 minutes and 20 seconds

4 hours and 0 minutes

3 minutes and 50 seconds

1 hour and 45 minutes

3 minutes and 20 seconds

Explanation:

Draw a right triangle with a height of 30,000 ft. and a base of 40,000 ft. The hypotenuse, or distance travelled, is then 50,000ft using the Pythagorean Theorem. Then dividing distance by speed will give us time, which is 200 seconds, or 3 minutes and 20 seconds.

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

A right triangle has two sides, 9 and x, and a hypotenuse of 15. What is x?

13

11

10

14

12

12

Explanation:

We can use the Pythagorean Theorem to solve for x.

92 + x2 = 152

81 + x2 = 225

x2 = 144

x = 12

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

The area of a right traingle is 42. One of the legs has a length of 12. What is the length of the other leg?

Explanation:

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

If  and , what is the length of ?

Explanation:

AB is the leg adjacent to Angle A and BC is the leg opposite Angle A.

Since we have a  triangle, the opposites sides of those angles will be in the ratio .

Here, we know the side opposite the sixty degree angle. Thus, we can set that value equal to .

which also means

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

Solve for x.

6

2

7

12

6

Explanation:

Use the Pythagorean Theorem. Let a = 8 and = 10 (because it is the hypotenuse)

### Example Question #11 : How To Find The Length Of The Side Of A Right Triangle

Solve for .

Explanation:

Use the Pythagorean Theorem to solve for the missing side of the right triangle.

In this triangle, .

Now we can solve for .

### Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Solve for .

Explanation:

This image depicts a 30-60-90 right triangle. The length of the side opposite the smallest angle is half the length of the hypotenuse.

### Example Question #13 : How To Find The Length Of The Side Of A Right Triangle

Given a right triangle, solve for the missing leg if one leg is 12 and the hypotenuse is 13.