Download Chapter 8 Resource Masters

NAME ______________________________________________ DATE
8-4
____________ PERIOD _____
Lesson Reading Guide
Trigonometry
Get Ready for the Lesson
Read the introduction to Lesson 8-4 in your textbook.
•
Why is it important to determine the relative positions accurately in navigation? (Give two
possible reasons.)
•
What does calibrated mean?
Read the Lesson
1. Refer to the figure. Write a ratio using the side lengths in the
figure to represent each of the following trigonometric ratios.
A. sin N
M
N
B. cos N
P
C. tan N
D. tan M
E. sin M
F. cos M
a. sin 20
i. the degree measure of an acute angle whose cosine is 0.8
b. cos 20
ii. the ratio of the length of the leg adjacent to the 20° angle to the
length of hypotenuse in a 20°-70°-90° triangle
c. sin⫺1 0.8
d. tan⫺1 0.8
e. tan 20
f. cos⫺1 0.8
iii.the degree measure of an acute angle in a right triangle for
which the ratio of the length of the opposite leg to the length of
the adjacent leg is 0.8
iv. the ratio of the length of the leg opposite the 20° angle to the
length of the leg adjacent to it in a 20°-70°-90° triangle
v. the ratio of the length of the leg opposite the 20° angle to the
length of hypotenuse in a 20°-70°-90° triangle
vi. the degree measure of an acute angle in a right triangle for
which the ratio of the length of the opposite leg to the length of
the hypotenuse is 0.8
Remember What You Learned
3. How can the co in cosine help you to remember the relationship between the sines and
cosines of the two acute angles of a right triangle?
Chapter 8
27
Glencoe Geometry
Lesson 8-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Assume that you enter each of the expressions in the list on the left into your calculator.
Match each of these expressions with a description from the list on the right to tell what
you are finding when you enter this expression.
NAME ______________________________________________ DATE
8-4
____________ PERIOD _____
Study Guide and Intervention
Trigonometry
Trigonometric Ratios
The ratio of the lengths of two sides of a right
triangle is called a trigonometric ratio. The three most common ratios
are sine, cosine, and tangent, which are abbreviated sin, cos, and tan,
respectively.
leg opposite ⬔R
hypotenuse
r
⫽ ᎏᎏ
t
sin R ⫽ ᎏᎏ
leg adjacent to ⬔R
cos R ⫽ ᎏᎏᎏ
hypotenuse
s
t
S
r
t
T
s
leg opposite ⬔R
tan R ⫽ ᎏᎏᎏ
leg adjacent to ⬔R
r
s
⫽ ᎏᎏ
⫽ ᎏᎏ
Example
Find sin A, cos A, and tan A. Express each ratio as
a decimal to the nearest thousandth.
B
13
5
C
opposite leg
hypotenuse
sin A ⫽ ᎏᎏ
adjacent leg
hypotenuse
cos A ⫽ ᎏᎏ
opposite leg
adjacent leg
⫽ ᎏᎏ
⫽ ᎏᎏ
12
13
⫽ ᎏᎏ
⬇ 0.923
⬇ 0.417
⫽ ᎏᎏ
⫽ ᎏᎏ
5
13
⬇ 0.385
A
12
tan A ⫽ ᎏᎏ
AC
AB
BC
AB
⫽ ᎏᎏ
R
BC
AC
5
12
Exercises
1. sin A
B
30
20
2. tan B
C
3. cos A
4. cos B
5. sin D
6. tan E
7. cos E
8. cos D
Chapter 8
E
34
28
16
A
D
16
12 F
Glencoe Geometry
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the indicated trigonometric ratio as a fraction
and as a decimal. If necessary, round to the nearest
ten-thousandth.
NAME ______________________________________________ DATE
8-4
Study Guide and Intervention
____________ PERIOD _____
(continued)
Trigonometry
Use Trigonometric Ratios
In a right triangle, if you know the measures of two sides
or if you know the measures of one side and an acute angle, then you can use trigonometric
ratios to find the measures of the missing sides or angles of the triangle.
Example
Find x, y, and z. Round each measure to the nearest
whole number.
A
z
B
a. Find x.
y
18
C
c. Find z.
b. Find y.
x ⫹ 58 ⫽ 90
x ⫽ 32
x⬚
58⬚
y
18
y
tan 58° ⫽ ᎏᎏ
18
18
z
18
cos 58° ⫽ ᎏᎏ
z
cos A ⫽ ᎏᎏ
tan A ⫽ ᎏᎏ
y ⫽ 18 tan 58°
y ⬇ 29
z cos 58° ⫽ 18
18
cos 58°
z ⫽ ᎏᎏ
z ⬇ 34
Exercises
1.
2.
x
3.
x⬚
16
12
28⬚
32
x⬚
4.
12
1
x⬚
5
Lesson 8-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find x. Round to the nearest tenth.
4
5.
40⬚
16
Chapter 8
6.
64⬚
15
x
29
x
Glencoe Geometry