EXAMPLE 4 Find a hypotenuse using an angle of depression

SKIING

You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21o. About how far do you ski down the mountain?

EXAMPLE 4 Find a hypotenuse using an angle of depression

SOLUTION

sin 21oWrite ratio for sine of 21o.

sin 21o Substitute.

x sin 21o = 1200 Multiply each side by x.

x = 1200. sin 21o Divide each side by sin 21o

x 1200. 0.3584

Use a calculator to find sin 21o

x 3348.2 Simplify.

opp hyp=

1200x=

ANSWER

You ski about 3348 meters down the mountain.

GUIDED PRACTICE for Example 4

6

Suppose the angle of depression in Example 4 is 28°. About how far would you ski?

WHAT IF ?

SOLUTION

sin 28oWrite ratio for sine of 28o.

sin 28o Substitute.

x sin 28o = 1200 Multiply each side by x.

x = 1200. sin 28o Divide each side by sin 28o

opp hyp=

1200x=

GUIDED PRACTICE for Examples 4

x 1200. 0.4694

Use a calculator to find sin 28o

x 2556m Simplify.