Pre-Algebra Chapter 9

Example 4
Use Trigonometric Ratios
to Solve a Problem
ARCHITECTURE The Leaning Tower
of Pisa in Pisa, Italy, tilts about 5.2°
from vertical. If the tower is 55 meters
tall, how far has its top shifted from
its original position?
x m
B C
55 m
5.2˚
Use the tangent ratio.
measure of leg opposite A
tan A
measure of leg adjacent to A
x
tan 5.2°
5 5
Write the tangent ratio.
Substitution
x
55(tan 5.2°) 55 Multiply each side by 55.
5 5
55 TAN 5.2 ENTER 5.00539211
5.0 x Simplify.
The top of the tower has shifted about 5.0 meters from its original position.
A
Concept Check
1. OPEN ENDED Compare and contrast the sine, cosine, and tangent ratios.
2. FIND THE ERROR Susan and Tadeo are finding the height of the hill.
Susan
x
sin 15° =
58 0
580(sin 15°) = x
150 x
Ta d e o
x
sin 15° =
56 0
560(sin 15°) = x
145 x
15˚
580 m
560 m
x m
Who is correct? Explain your reasoning.
Guided Practice
Find each sine, cosine, or tangent. Round to four
decimal places, if necessary.
3. sin N
4. cos N
5. tan N
N
8
M
15
17
P
Application
Use a calculator to find each value to the nearest ten thousandth.
6. sin 52° 7. cos 19° 8. tan 76°
For each triangle, find each missing measure to the nearest tenth.
9. x
10. 11.
53˚
www.pre-alg.com/extra_examples
32
21˚
73
12. RECREATION Miranda is flying a kite on a 50-yard string, which makes a
50° angle with the ground. How high above the ground is the kite?
x
x
Lesson 9-8 Sine, Cosine, and Tangent Ratios 479
12
33˚