1. Use the tangent of an acute angle to find a leg length.
EXAMPLE 2
Find a leg length
ALGEBRA
Find the value of x.
SOLUTION
Use 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

2. Estimate height using tangent
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.
Multiply each side by 40.
40 tan 70o
= h
Use a calculator to simplify.
109.9 h
ANSWER
The lamppost is about 110 inches tall.

3. Find the value of x. Round to the nearest tenth.
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.
x tan 61o
= 22
Multiply each side by x. x
12.2 =
Simplify.

4. Find the value of x. Round to the nearest tenth.
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.
13 tan 56o
= x
Multiply each side by 13.
19.3 x =
Simplify.

5. Find leg lengths using an angle of elevation
EXAMPLE 5
Find leg lengths using an angle of elevation
SOLUTION
STEP 1
Find the height.
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.
ANSWER
The height is about 6.1 feet.

6. Find leg lengths using an angle of elevation
EXAMPLE 5
Find leg lengths using an angle of elevation
STEP 2
Find the length of the base.
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.
ANSWER
The length of the base is about 12.6 feet.

7. Angle of elevation

8. Angle of depression

9. 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?