# Lesson 8 - Glencoe

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```Lesson 9-8
Example 1 Find Trigonometric Ratios
Find sin C, cos C, and tan C.
measure of leg opposite angle C
measure of hypotenuse
6
=
or 0.60
10
sin C =
measure of leg adjacent to angle C
measure of hypotenuse
8
=
or 0.80
10
cos C =
measure of leg opposite angle C
measure of leg adjacent to angle C
6
= or 0.75
8
tan C =
Example 2 Use a Calculator to Find Trigonometric Ratios
Find each value to the nearest ten thousandth.
a. sin 68°°
SIN 68 ENTER 0.9271838546
So, sin 68° is about 0.9272.
b. cos 21°°
COS 21 ENTER 0.9335804265
So, cos 21° is about 0.9336.
c. tan 87°°
TAN 87 ENTER 19.08113669
So, tan 87° is about 19.0811.
Example 3 Use Trigonometric Ratios
Find the missing measure. Round to the nearest tenth.
The measures of an acute angle and the hypotenuse are known. You need to find the
measure of the side adjacent to the angle. Use the cosine ratio.
measure of leg adjacent to angle C
measure of hypotenuse
x
cos 28° =
52
52(cos 28°) = x
52 × COS 28 ENTER 45.91327483
45.9 ≈ x
cos ∠ C =
Write the cosine ratio.
Substitution
Multiply each side by 52.
Simplify.
The measure of the side adjacent to the acute angle is about 45.9 feet.
Example 4 Use Trigonometric Ratios to Solve a Problem
NATURE
A tree has grown in such a way that its trunk tilts about 12.3°°
from vertical. If the tree is 48 feet tall, how far has its top shifted from its original
position?
Use the tangent ratio.
measure of leg opposite angle A
measure of leg adjacent to angle A
x
tan 12.3° =
48
48(tan 12.3°) = x
48 × TAN 12.3 ENTER 10.4656925
10.5 ≈ x
tan ∠A =
Write the tangent ratio.
Substitution
Multiply each side by 48.
Simplify.
The top of the tree trunk has shifted about 10.5 feet from a vertical position.
```