Download 11-5 The Trigonometric Ratios

11-5 The Trigonometric Ratios
Name
Date
Find the sine, cosine, and tangent of ⬔A to the nearest ten-thousandth.
B
length of leg opposite ⬔A 21
sin A ⫽
⫽
艐 0.7241
29
length of hypotenuse
cos A ⫽
length of leg adjacent to ⬔A 20
⫽
艐 0.6897
29
length of hypotenuse
tan A ⫽
length of leg opposite ⬔A
⫽ 21 ⫽ 1.0500
length of leg adjacent to ⬔A 20
29
A
21
20
C
Find the sine, cosine, and tangent of the indicated angle to the
nearest ten-thousandth.
1. ⬔A
117
sin A 125 0.9360
44
cos A 125 0.3520
117
tan A 44 艐 2.6591
3. ⬔F
1.53
艐 0.8270
1.85
1.04
cos F 艐 0.5622
1.85
1.53
tan F 艐 1.4712
1.04
Copyright © by William H. Sadlier, Inc. All rights reserved.
sin F 5. ⬔X
1.6
艐 0.9756
1.64
0.36
艐 0.2195
cos X 1.64
1.6
艐 4.4444
tan X 0.36
sin X 7. ⬔L
12
艐 0.9231
13
5
艐 0.3846
cos L 13
12
tan L 2.4000
5
sin L 2. ⬔B
B
44
0.3520
125
117
cos B 0.9360
125
44
tan B 艐 0.3761
117
sin B 125
117
A
C
44
4. ⬔G
1.04
艐 0.5622
1.85
1.53
艐 0.8270
cos G 1.85
1.04
艐 0.6797
tan G 1.53
G
sin G 1.53
1.85
F
6. ⬔Y
0.36
艐 0.2195
1.64
1.6
艐 0.9756
cos Y 1.64
0.36
tan Y 0.2250
1.6
sin Y Y
1.64
X
5
艐 0.3846
13
12
艐 0.9231
cos M 13
5
艐 0.4167
tan M 12
Lesson 11-5, pages 290–291.
1.6
0.36
8. ⬔M
sin M H
1.04
Z
M
13
L
12
5
N
Chapter 11 285
For More Practice Go To:
You can use a handheld device to find the sine, cosine, and tangent of
the given angle to the nearest ten-thousandth.
9. 49⬚
10. 84⬚
11. 12⬚
1
49
sin 49 艐 0.7547
49
cos 49 艐 0.6561
49
tan 49 艐 1.1504
12. 45⬚
sin 84 艐 0.9945
cos 84 艐 0.1045
tan 84 艐 9.5144
13. 23.5⬚
sin 45 艐 0.7071
cos 45 艐 0.7071
tan 45 1.0000
sin 12 艐 0.2079
cos 12 艐 0.9781
tan 12 艐 0.2126
14. 76.8⬚
sin 23.5 艐 0.3987
cos 23.5 艐 0.9171
tan 23.5 艐 0.4348
sin 76.8 艐 0.9736
cos 76.8 艐 0.2284
tan 76.8 艐 4.2635
Use a handheld to find the measure of ⬔A to the nearest degree.
15. sin A ⫽ 0.5624
17. cos A ⫽ 0.4836
0.5624
34
18. cos A ⫽ 0.0025
68
19. tan A ⫽ 3.5123
90
21. Manny is making a corner shelf. The legs
of the right triangle are 17 cm and 20 cm.
What is the measure of the smallest angle
of the triangle?
17
0.85
20
so m⬔A 40.3645. . . 艐 40
20
艐 1.1765; m⬔B 49.6362. . . 艐 50
tan B 17
The angles are 40, 50, and 90
The smallest angle measures about 40.
Make a drawing; tan A 61
20. tan A ⫽ 8.9652
84
74
22. A rectangular playground is 25 ft long. Josh
constructs a 30-foot fence along its diagonal.
What is the measure of the angle between the
fence and the side that represents the length
of the playground?
25
艐 0.8333;
30
m⬔A 33.5573. . . 艐 34; The angle is about 34.
Make a drawing; cos A 23. On paper or a handheld, compare sin 75⬚ with cos 15⬚. Then compare the sine
and cosine of other angles that have a sum of 90⬚. Explain what you discover.
sin 75 艐 0.9659; cos 15 艐 0.9659; so sin 75 cos 15; Students will see from their results that
for any pair of angles whose sum is 90, sin A cos (90 A), where A is one of the angles.
286 Chapter 11
Copyright © by William H. Sadlier, Inc. All rights reserved.
1
16. sin A ⫽ 0.9253