Download 11-6 Use Trigonometric Ratios to Solve Right Triangles

11-6 Use Trigonometric Ratios to Solve Right Triangles
Name
Date
Solve 䉭ABC. Round the length of the side to the nearest tenth.
m⬔A 22°
m⬔B 90 22°
The acute angles of a right triangle
B
29.5
are complementary.
68°
A
Find the measure of b to the nearest tenth.
length of adjacent leg
cos A Decide which ratio to use.
length of hypotenuse
Substitute the given values.
cos 22° b
29.5
0.9272 艐 b
Use a handheld to find cos 22°.
29.5
b 艐 0.9272(29.5)
Use the cross products.
b 艐 27.4
11.2
22°
C
b
Remember: The handheld
must be in the degree mode
and in the approximate mode.
Solve each right triangle. Round the lengths of the sides to the nearest tenth
and the angle measures to the nearest degree.
B
1.
c
Copyright © by William H. Sadlier, Inc. All rights reserved.
A
c
9.5
C
34.8
A
9.5
tan A 34.8 0.2730
⬔A 15°; m⬔B 75°
(9.5)2 (34.8)2 c 2
1301.29 c 2
36.1 c
m⬔A 15°; m⬔B 75°; c 36.1
B
3.
A
B
2.
3.4
0.2957
11.5
⬔A 16°; m⬔B 74°
(3.4)2 (11.5)2 c2
143.81 c2; 12.0 c
m⬔A 16°; m⬔B 74°; c 12.0
tan A B
4.
19
32.03
14
C
A
19
1.3571
14
⬔A 54°; m⬔B 36°
(19)2 (14)2 c2
557 c2; 23.6 c
m⬔A 54°; m⬔B 36°; c 23.6
C
11.5
c
tan A 3.4
62°
15
a
C
a
32
0.8829(32) a
28.2528 a
a 28.3
sin 62° Lesson 11-6, pages 292–293.
Chapter 11 287
For More Practice Go To:
Solve each right triangle. Round the lengths of the sides to the nearest tenth
and the angle measures to the nearest degree.
B
5.
B
6.
31°
42°
A
c
28
A
C
b
b
; b 0.9004(28) 25.2
28
2
2
c 28 25.22; c2 1419.04; c 37.7
m⬔A 90 42 48
m⬔A 48°; b 25.2; c 37.7
B
C
b
b
; b 0.6009(25) 15.0
25
2
2
c 25 15.02; c2 850; c 29.2
m⬔A 90 31 59
m⬔A 59°; b 15.0; c 29.2
tan 42 7.
25
tan 31 B
8.
62°
55°
c
A
54.8
A
C
9. Parag folds paper to make figures.
He made a boat shaped like a right triangle
5
with 8 -ft and 1-ft legs. What are the
measures of the triangle’s acute angles?
Round to the nearest degree.
Make a drawing; tan A 1 1.6; m⬔A 58
5
8
5
90 58 32 OR tan A 8 0.625.
1
m⬔A 32; 90 32 58
The acute angles have measures of 32° and 58.
x8
288 Chapter 11
a
49.3
C
a
m⬔A 90 55 35
a
tan 35 ; a 0.7002(54.8) 38.4
54.8
c2 54.82 38.42; c2 4477.6; c 66.9
m⬔A 35°; a 38.4; c 66.9
11. Solve: 1 2
4 x
c
12. Solve: 5 1
x 9
x 45
m⬔A 90 62 28
a
tan 28 ; a 0.5317(49.3) 26.2
49.3
c2 49.32 26.22; c2 3116.93; c 55.8
m⬔A 28°; a 26.2; c 55.8
10. Ted cuts a rectangular board that is
131 in. long and 75 in. wide along the diagonal
to make supports for a table. What are the
measures of the angles along the cut?
131
1.75
75
m⬔A 60; m⬔B 90 60 30
75
OR tan A 0.5725; m⬔A 30
131
m⬔B 90 30 60
The angles along the cut measure 60° and 30°.
Make a drawing; tan A 13. Solve: 3 2
x 5
15
x 2
14. Solve: 11 8
7
x
56
x 11
Copyright © by William H. Sadlier, Inc. All rights reserved.
c