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

## Example Questions

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

A right triangle has one side equal to 5 and its hypotenuse equal to 14. Its third side is equal to:

171

13.07

9

12

14.87

13.07

Explanation:

The Pythagorean Theorem gives us a2 + b2 = c2 for a right triangle, where c is the hypotenuse and a and b are the smaller sides. Here a is equal to 5 and c is equal to 14, so b2 = 142 – 52 = 171. Therefore b is equal to the square root of 171 or approximately 13.07.

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

Which of the following could NOT be the lengths of the sides of a right triangle?

5, 7, 10

14, 48, 50

8, 15, 17

12, 16, 20

5, 12, 13

5, 7, 10

Explanation:

We use the Pythagorean Theorem and we calculate that 25 + 49 is not equal to 100.
All of the other answer choices observe the theorem a2 + b2 = c2

### Example Question #102 : Sat Mathematics

Which set of sides could make a right triangle?

10, 12, 16

4, 6, 9

6, 7, 8

9, 12, 15

9, 12, 15

Explanation:

By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.

### Example Question #1 : 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

5.5

5

4

3.5

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 #1 : 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

12 √6

33√2

33

42

15

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 #1 : 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

1 hour and 45 minutes

3 minutes and 20 seconds

4 hours and 0 minutes

3 minutes and 50 seconds

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 #1 : 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?

11

14

12

10

13

12

Explanation:

We can use the Pythagorean Theorem to solve for x.

92 + x2 = 152

81 + x2 = 225

x2 = 144

x = 12

### Example Question #2 : 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 #11 : 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 #1 : How To Find The Length Of The Side Of A Right Triangle Solve for x.

12

2

6

7

6

Explanation:

Use the Pythagorean Theorem. Let a = 8 and = 10 (because it is the hypotenuse)     ← Previous 1

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