EXAMPLE 1 Using a 45o–45o–90o Triangle

Softball

The infield of a softball field is a square with a side length of 60 feet. A catcher throws the ball from home plate to second base. How far does the catcher have to throw the ball?

SOLUTION

To find the distance, use the rule for a 45o–45o–90o triangle.

EXAMPLE 1

hypotenuse = leg 2

= 60 2

60(1.414)

= 84.84

A catcher has to throw the ball about 85 feet.

ANSWER

Using a 45o–45o–90o Triangle

GUIDED PRACTICE for Example 1

1. A city park is shaped like a square with a side length of 150 feet. What is the distance diagonally across the park?

City Parks

ANSWER

The distance diagonally across the park is about 212 ft

EXAMPLE 2 Using a 30o–60o–90o Triangle

Find the value of each variable in the triangle. Give the exact answer.

You need to find the length of the shorter leg first in order to find the length of the longer leg.

STEP 1

Find the length of the shorter leg.

hypotenuse = 2 shorter leg

= 10 2 x =5 x

Rule for 30o–60o–90o triangle

Substitute.

Divide each side by 2.

EXAMPLE 2

STEP 2

Find the length of the longer leg.

Rule for 30o–60o–90o triangle

Substitute.

3longer leg = shorter leg

= 3y 5

The shorter leg is 5 units long. The longer leg is 5 units long.

3

ANSWER

Using a 30o–60o–90 Triangle

GUIDED PRACTICE for Example 2

Find the value of each variable. Give the exact answer.

2.

ANSWER

The value for x = 25 in. y = in. 25 3

GUIDED PRACTICE for Example 2

3.

ANSWER

The value for x = 7m, y = 14m

GUIDED PRACTICE for Example 2

4.

ANSWER

The value for x = 2cm and y = 2 cm3

EXAMPLE 3 Rotating 180

The pyramid ski show is a common attraction at water parks. Find the horizontal distance from the pyramid to the boat.

Water Ski Show

STEP 1

Find the length of the shorter leg.

hypotenuse = 2 shorter leg

= 26 2 x =13 x

EXAMPLE 3

STEP 2

Find the length of the longer leg.

longer leg = shorter leg 3

The horizontal distance is about 23 feet.

ANSWER

= 3y 13

22.52

Using a Special Right Triangle

GUIDED PRACTICE for Example 3

5. What If?

3In Example 3, suppose that the horizontal distance from the pyramid to the boat is 15 feet. What is the distance from the top of the pyramid to the boat?

ANSWER

The distance from the top of the pyramid to the boat is 30 ft.