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Law of sines, cosines and area

Total questions: 13

Worksheet time: 59mins

Name
Class
Date
1.
Which of the following formulas shows the Law of Cosines?
a)
c2 = a2 + b2 - 4ac + cosA
b)
c2 = a2 - b2 - 2abcosC
c)
c2 = a2 + b2 - 2abcosC
d)
(cos A)/a = (cos B)/b
2.
Which Law would you use?
a)
Law of Sines
b)
Law of Cosines
c)
Law of the Jungle
d)
Law of Gravity
3.
Which Law would you use?
a)
Law of Sines
b)
Law of Cosines
c)
Law of the Jungle
d)
Law of Gravity
4.

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, to 2 decimal places, is the bird from Amanda?

a)

25.23 ft

b)

23.19 ft

c)

22.15 ft

d)

20.85 ft

5.
a)

A

b)

B

c)

C

d)

D

6.
Jack is flying his kite.  He runs 100 feet away from his house and lets out 75 feet of string.  The angle of elevation from the ground to the kite is 65 degrees.  How far away is the kite from the house?
a)
9285.73 ft
b)
96.36 ft
c)
24061.81 ft
d)
155.12 ft
7.
How many triangles can you make if A=53, b=6, and a=5?
a)
0
b)
1
c)
2
d)
Infinitely many
8.

If the sides of a triangle are 12,5, and 2. What is the area?

a)

12

b)

40.65

c)

19

d)

This triangle does not exist

9.

Find the length of side AB.

a)

10

b)

8

c)

6.1

d)

4.9

10.

What is the area of this triangle to three decimal places?

a)

14.494 meters squared

b)

108.184 meters squared

c)

54.092 meters squared

d)

54.350 meters squared

11.

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

12.
Parker must find the distance from Point A to Point B on opposite sides of a lake.  He locates Point C that is 860 feet from point A and 175 feet from Point B.  He measures the angle at Point C to be 78 degrees.  Find the distance from point A to point B.
a)
707643.58
b)
841.22
c)
877.62
d)
842.01
13.
What is the measure of angle A?
a)
50 degrees
b)
60 degrees
c)
78 degrees
d)
74 degrees