Law of Sines / Cosines Review

Name: ________________________ Class: ___________________ Date: __________
Law of Sines / Cosines Review - Part 1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Use the Law of Sines. Find b to the nearest tenth.
a.
____
b.
41.6
c.
18.6
d.
23.1
d.
73.8°
d.
75°
2. Use the Law of Sines. Find m∠C to the nearest tenth.
a.
____
47.3
106.2°
b.
118.1°
c.
61.9°
3. In ∆JKL, j = 9 in., k = 5 in., and m∠L = 43°. Find m∠J .
a.
28°
b.
59°
c.
1
32°
ID: A
Name: ________________________
____
4. In ∆FGH , g = 8 ft, h = 13 ft, and m∠F = 72°. Find m∠G. Round your answer to the nearest tenth.
a.
____
26.2°
b.
35.9°
c.
72.1°
d.
32.5°
132.9
d.
63.2
d.
85.7°
5. Use the Law of Cosines. Find b to the nearest tenth.
a.
____
ID: A
102.2
b.
62.4
c.
6. Use the Law of Cosines. Find m∠A to the nearest tenth of a degree.
a.
33.9°
b.
57.7°
c.
2
46.3°
Name: ________________________
____
7. On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 216
feet deep. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the
right of the pitcher’s mound. An outfielder catches the ball and throws it to the pitcher. How far does the
outfielder throw the ball?
a.
____
ID: A
207.4 ft
b.
224.3 ft
c.
169.3 ft
d.
198.7 ft
d.
12.1 m2
8. Find the area of the triangle. Round your answer to the nearest tenth.
a.
9.2 m2
b.
6.0 m2
c.
3
8 m2
Name: ________________________
ID: A
Short Answer
9. A plane is located at C on the diagram. There are two towers located at A and B. The distance between the
towers is 1,600 feet, and the angles of elevation are given.
a. Find BC, the distance from Tower 2 to the plane, to the nearest foot.
b. Find CD, the height of the plane from the ground, to the nearest foot.
Find the remaining sides and angles in the triangle. Round your answers to the nearest tenth.
10. m∠A = 55°, m∠B = 44°, and b = 68
____|____|____
|
|
4
Name: ________________________
ID: A
11. a = 11, b = 12, and c = 17
____|____|____
|
|
12. Use the Law of Sines to solve the triangle
____|____|____
|
|
5
Name: ________________________
ID: A
13. Use the Law of Cosines and Sines to solve the triangle.
____|____|____
|
|
14. A farmer is estimating the surface area of his barn to find how much paint he needs to buy. One part of the
barn is triangular as shown.
a. The darkened sides in the figure are the edges of the roof. This trim will be painted white. Find the length
of each of these two sides of the triangle.
b. The triangular surface will be painted red. Find the area of the triangle.
6
ID: A
Law of Sines / Cosines Review - Part 1
Answer Section
MULTIPLE CHOICE
1. ANS:
KEY:
2. ANS:
KEY:
3. ANS:
KEY:
4. ANS:
KEY:
5. ANS:
KEY:
6. ANS:
KEY:
7. ANS:
KEY:
8. ANS:
KEY:
D
REF: 14-4 Area and the Law of Sines
TOP:
Law of Sines
D
REF: 14-4 Area and the Law of Sines
TOP:
Law of Sines
D
REF: 14-5 The Law of Cosines
TOP:
Law of Cosines | Law of Sines | finding an angle of a triangle
B
REF: 14-5 The Law of Cosines
TOP:
Law of Cosines | Law of Sines
D
REF: 14-5 The Law of Cosines
TOP:
Law of Cosines
A
REF: 14-5 The Law of Cosines
TOP:
Law of Cosines
C
REF: 14-5 The Law of Cosines
TOP:
Law of Cosines | problem solving
B
REF: 14-4 Area and the Law of Sines
TOP:
area and the Law of Sines
SHORT ANSWER
9. ANS:
a. about 2,433 feet
b. about 1,325 feet
REF: 14-4 Area and the Law of Sines
TOP: 14-4 Example 4
KEY: Law of Sines | multi-part question | problem solving
10. ANS:
m∠C = 81°, a = 80.2, c = 96.7
REF: 14-4 Area and the Law of Sines
TOP: 14-4 Example 3
KEY: Law of Sines | finding an angle of a triangle
11. ANS:
m∠A = 40.1°, m∠B = 44.7°, m∠C = 95.2°
REF: 14-5 The Law of Cosines
TOP: 14-5 Example 2
KEY: Law of Cosines | finding an angle of a triangle
12. ANS:
56.1
REF: 14-4 Area and the Law of Sines
KEY: Law of Sines
TOP: 14-4 Example 2
1
14-4 Example 2
14-4 Example 2
14-5 Example 3
14-5 Example 3
14-5 Example 1
14-5 Example 2
14-5 Example 1
14-4 Example 1
ID: A
13. ANS:
22.0
REF: 14-5 The Law of Cosines
TOP: 14-5 Example 1
KEY: Law of Cosines
14. ANS:
a. To find the lengths of the sides, first find the angle at the top and then use the Law of Sines to find the
length of one side. The sides are equal in length since the triangle is isosceles.
The sum of the angles of a triangle is 180°.
180° − 2(30°) = 120°
The top angle measures 120°. Now use the Law of Sines and solve for d.
d
22
=
sin 30°
sin 120°
22(sin 30°)
d =
sin 120
d ≈ 12.7
The length of each side is about 12.7 meters.
1
b. To find the area of the triangle, you must find the height of the triangle. Then the area is bh.
2
h
sin 30° =
12.7
h = (sin 30°)(12.7)
Area ≈ 0.5(sin 30°)(12.7)(22) ≈ 69.9
The area of the triangle is about 69.9 square meters.
REF: 14-4 Area and the Law of Sines
TOP: 14-4 Example 2
KEY: area and the Law of Sines | Law of Sines | multi-part question | problem solving | writing in math
2