```Name ________________________________________ Date __________________ Class __________________
Reteach
Law of Sines and Law of Cosines
You can use a calculator to find trigonometric ratios for obtuse angles.
sin 115
0.906307787
cos 270
0
tan 96
9.514364454
The Law of Sines
For any ABC with side lengths a, b, and c that are
opposite angles A, B, and C, respectively,
sin A sin B sin C
.
a
b
c
Find m P. Round to the nearest degree.
sin P
MN
sin N
PM
Law of Sines
sin P
10 in.
sin36
7 in.
MN
sin36
7 in.
10, m N
36 , PM
7
Multiply both sides by 10 in.
sin P
10 in.
sin P
0.84
m P
1
sin (0.84)
Use the inverse sine function to find m P.
m P
57
Simplify.
Simplify.
Use a calculator to find each trigonometric ratio. Round to the nearest
hundredth.
1. cos 104
________________________
2. tan 225
3. sin 100
_________________________
________________________
Find each measure. Round the length to the nearest tenth and the
angle measure to the nearest degree.
4. TU
_________________________________________
5. m E
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name ________________________________________ Date __________________ Class __________________
Reteach
Law of Sines and Law of Cosines continued
The Law of Cosines
For any ABC with side lengths a, b, and c that are
opposite angles A, B, and C, respectively,
a2 b2 c 2
b2 a2 c 2
c 2 a2 b2
2bc cos A,
2ac cos B,
2ab cos C.
Find HK. Round to the nearest tenth.
HK 2
HK
2
HK
HJ 2
JK 2
289
196
179.0331 ft
2(HJ)(JK) cos J
Law of Cosines
2(17)(14) cos 50
Substitute the known values.
2
13.4 ft
Simplify.
Find the square root of both sides.
You can use the Law of Sines and the Law of Cosines to solve triangles according
to the information you have.
Use the Law of Sines if you know
• two angle measures and any side length, or
• two side lengths and a nonincluded angle
measure
Use the Law of Cosines if you know
• two side lengths and the included angle
measure, or
• three side lengths
Find each measure. Round lengths to the nearest tenth and angle
measures to the nearest degree.
6. EF
_________________________________________
8. m R
_________________________________________
7. m X
________________________________________
9. AB
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name ________________________________________ Date __________________ Class __________________
4.
1. Law of Cosines
2. Law of Sines
3. Law of Cosines
4. 8 ft
5. 55
VECTORS
5.
2 2
;
;1
2 2
6.
2
;
2
2
; 1
2
7. Possible answer: The sine of an angle
is equal to the cosine of the angle’s
complement: sin A cos (90 A).
Reteach
1.
Practice A
1. vector
2. direction
3. length
4. parallel
5. equal
6. 3, 4
7. 9, 5
8. 5, 4
9. 5
0.24
2. 1
3. 0.98
4. 24.7 m
5. 37
6. 7.0 cm
7. 58
8. 45
9. 8.1 km
Challenge
1. ABC, DAE, FCE, BDF
2. 28
10. 7.3
3. 40
4. 112
sin 28
20.5m
5.
sin 40
h
6. 28.1 m
7.
11. 45°
8. tan 62
28.1m
x
9. 14.9 m
Problem Solving
12. 14°
1. 23.3 mi
2. 32.9 ft
3. 122°
4. 60°
5. C
6. G
7. B
8. H
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
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