EXAMPLE 2 Find a leg lengthALGEBRA Find the value of x.

SOLUTIONUse the tangent of an acute angle to find a leg length.

tan 32o =opp. adj. Write ratio for tangent of 32o.

tan 32o 11

=x

Substitute.

x tan 32o = 11 Multiply each side by x.

x = 11 tan 32o Divide each side by tan 32o

x 11 0.6249

Use a calculator to find tan 32o

x 17.6 Simplify

EXAMPLE 3 Estimate height using tangent

LAMPPOST

Find the height h of the lamppost to the nearest inch.

tan 70o =opp. adj. Write ratio for

tangent of 70o.

tan 70o h.

=40.

Substitute.

40 tan 70o = hMultiply each side by 40.

109.9 h Use a calculator to simplify.

ANSWER

The lamppost is about 110 inches tall.

GUIDED PRACTICE for Examples 2, 3, and 4

Find the value of x. Round to the nearest tenth.

tan 61o =opp. adj. Write ratio for tangent of 60o.

tan 61o 22

= x

Substitute.

Multiply each side by x. x tan 61o = 22

x 12.2 = Simplify.

GUIDED PRACTICE for Examples 2, 3, and 4

Find the value of x. Round to the nearest tenth.

tan 56o =opp. adj. Write ratio for tangent of 56o.

tan 56o x=13

Substitute.

Multiply each side by 13.13 tan 56o = x

19.3 x = Simplify.

EXAMPLE 5 Find leg lengths using an angle of elevation

SOLUTION

sin 26o =opp. hyp. Write ratio for sine of 26o.

sin 26o x

=14 Substitute.

14 sin 26o = x Multiply each side by 14.

6.1 x Use a calculator to simplify.

STEP 1 Find the height.

ANSWERThe height is about 6.1 feet.

EXAMPLE 5 Find leg lengths using an angle of elevation

cos 26o =adj. hyp. Write ratio for cosine of 26o.

cos 26o y

=14 Substitute.

14 cos 26o = x Multiply each side by 14.

12.6 x Use a calculator to simplify.

STEP 2 Find the length of the base.

ANSWER

The length of the base is about 12.6 feet.

ANGLE OF ELEVATION

ANGLE OF DEPRESSION

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?