EXAMPLE 1 Find the length of a hypotenuse

SOLUTION

Find the length of the hypotenuse of the right triangle.

(hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem

x2 = 62 + 82

x2 = 36 + 64

x2 = 100

x = 10 Find the positive square root.

Substitute.

Multiply.

Add.

GUIDED PRACTICE for Example 1

Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form.

1.

SOLUTION

(hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem

52 = 62 + 42

25= 9 + x2

x2 = 16

x = 4 Find the positive square root.

Substitute.

Multiply.

Subtract 9 from both sides

Leg;4

GUIDED PRACTICE for Example 1

Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form.

2.

SOLUTION

(hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem

x2 = 62 + 42

x2 = 36 + 16

x2 = 52

Find the positive square root.

Substitute.

Multiply.

Add.

x = 2 13

hypotenuse; 2 13