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Law of Sines/Cosines

Total questions: 28

Worksheet time: 1hrs 11mins

Name
Class
Date
1.

What are the possible criteria for Law of Sines?

a)

SSA, ASA, AAS

b)

AAS, SSS, ASA

c)

SAS, SSS, ASA

d)

SAS, AAS, ASA

2.

What are the possible criteria for the Law of Cosines?

a)

SSA, SSS

b)

SSA, ASA

c)

SSS, SAS

d)

AAS, ASA

3.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

4.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

5.
Find m<B
a)
A
b)
B
c)
C
d)
D
6.
Find BC
a)
A
b)
B
c)
C
d)
D
7.
Find m<A
a)
A
b)
B
c)
C
d)
D
8.
Find m<C
a)
A
b)
B
c)
C
d)
D
9.
Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them.  The angle of elevation from Amanda to the bird is 55 degrees, and from Jamie to the bird is 63 degrees.  How far away is the bird from Amanda?
a)
25.23
b)
23.19
c)
22.15
d)
20.85
10.

Two stakes are holding a small blimp in place. Stake A measures an angle of elevation of 49o and Stake B measures an angle of elevation of 58o. If the string attached to Stake A has a length of 148 feet, what is the length of the string attached to Stake B?

a)

152.7 feet

b)

166.3 feet

c)

157.3 feet

d)

131.7 feet

11.

Mr. Creole must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 4.15 miles from point A and 5.33 miles from Point B. He measures the angle ACB to be 37o. Find the distance from point A to point B.

a)

3.72 miles

b)

6.18 miles

c)

10.30 miles

d)

3.21 miles

12.

In an effort to recover Abraham's lost cell phone, two cell towers stationed 6000 feet apart detect the signal from the phone. Using strength of signal, the west tower measures the phone to be 5050 feet away and the east tower detects the phone to be 2420 feet away (see diagram). What angle  θ\theta  should Abraham walk from the west tower to get to his phone?

a)

θ=18.48°\theta=18.48\degree  

b)

θ=23.33°\theta=23.33\degree  

c)

θ=24.17°\theta=24.17\degree  

d)

θ=27.91°\theta=27.91\degree  

13.

A GPS satellite measures the distances to two buildings to be 370 km and 350 km, and the angle between them to be 2.1o (see diagram). How far apart are the two buildings?

a)

17.90 km

b)

30.32 km

c)

15.61 km

d)

23.96 km

14.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

15.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

16.

What is the reference angle?

a)

163

b)

73

c)

27

d)

107

17.
Negative angles are measured in which direction from standard position?
a)
Clockwise
b)
Counterclockwise
18.
Positive angles are measured in which direction from standard position?
a)
Clockwise
b)
Counterclockwise
19.

In which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

20.

Find a coterminal angle to 5°.

a)

365°

b)

255°

c)

-220°

d)

-365°

21.

What are the negative and positive coterminal angles of 240°?

a)

540°, -120°

b)

600°, -120°

c)

425°, -240°

d)

120°, -135°

22.
Convert 150⁰ to radians
a)
5π/6
b)
3π/4
c)
7π/6
d)
2π/3
23.
What is 7π/4 radians in degrees?
a)
300
b)
135
c)
315
d)
45
24.
What is 2π/3 radians in degrees? 
a)
150
b)
120
c)
180
d)
 30
25.
Convert the following to radians:   
720⁰
a)
b)
c)
26.

The length of an arc is 18cm and the radius of the circle is 6cm. What is the radian measure of the central angle?

a)

3 radian

b)

2 radian

c)

4 radian

d)

2π radian

27.

A central angle measure 4.5 radians and has an arc of 35 inches. What is the radius of the circle?

a)

7.78 inches

b)

8.21 inches

c)

157.5 inches

d)

7 inches

28.

Find the arc length.

a)

3π/4 ft

b)

39π/4 ft

c)

13π/4 ft

d)

4π/13 ft