Free Printable Law of sines-Cosines

1.

Use the Law of Sines to solve for BC

a)

33

b)

24

c)

12

d)

29

2.

Find m<B

a)

A

b)

B

c)

C

d)

D

3.

Solve for x.

a)

24.3

b)

155.7

c)

24.3 and 155.7

d)

not possible.

4.

Solve each triangle. A=40, B=20, a=2

a)

C=120, b=1.06, c=2.69

b)

C=135, b= 1.56, c=2.50

c)

C= 120, b=2.68. c=3.26

d)

C=45, b=1.06, c=2

5.

Find the area of the triangle.

a)

88 square units

b)

108 square units

c)

63 square units

d)

148 square units

6.

Find angle Z

a)

20.15°

b)

71.23°

c)

51.06°

d)

57.71°

7.

Find m<C

a)

A

b)

B

c)

C

d)

D

8.

Find QR

a)

34.7 km

b)

2.2 km

c)

13.74

d)

31.1 km

9.

Use the Law of Cosines to find the value of x. (Level 1)

a)

41.7

b)

51.7

c)

61.7

d)

71.7

10.

Which of the following could have a second triangle associated with it?

a)

b)

c)

d)

11.

Solve the triangle
$C=103\degree,\ b=16cm,\ c=12cm$

a)

$A=67\degree,\ B=73\degree,\ a=5.7cm$ or $A=33\degree,\ B=107\degree,\ a=3.5cm$

b)

$A=65.4\degree,\ B=74.6\degree,\ a=5.7cm$ or $A=34.6\degree,\ B=105.4\degree,\ a=3.5cm$

c)

Not a triangle

d)

$A=65.4\degree,\ B=74.6\degree,\ a=7cm$ or $A=34.6\degree,\ B=105.4\degree,\ a=5cm$

12.

Solve the Triangle(s): A = 26^o, a = 5, b = 9

a)

no triangle possible

b)

B = 14^o, C = 21^o, c = 8.7

c)

B = 52^o, C = 102^o, c = 11.2

d)

B = 52^o , C = 102^o, c = 11.2

OR

B = 128^o, C = 26^o, c = 5.0

13.

State the number of possible triangles that can be formed using the given measurements.
$B=147\degree,\ a=25\ km,\ b=15\ km$

a)

Two Triangles

b)

One Triangle

c)

None

14.

Find AB

a)

10.03

b)

8.04

c)

6.10

d)

4.93

15.

$\left(1-\cos^2\theta\right)Csc^2\theta$ Simplify the expression

a)

$\cos\theta$

b)

$\sin\theta$

c)

$\cot\theta$

d)

0

16.

$Cos^2\theta\ +\cos^2\theta\tan^2\theta$ Simplify the expression

a)

1

b)

0

c)

6

d)

3

17.

Choose the correct ratio.

a)

A

b)

B

c)

C

d)

D

18.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

19.

What is the correct equation to solve for x ?

a)

tan( 46 ) = 17/x

b)

sin ( 46 ) = x/17

c)

tan (46 ) = x/17

d)

cos (46) = x/17

20.

Find the length of side AC.

a)

25.4

b)

24.7

c)

29.2

d)

28.3

21.

Solve for the missing angle.

a)

32°

b)

44°

c)

61°

d)

50°

22.

Find the measure of the indicated angle (?) round to the nearest tenth.

a)

9.4

b)

55.2

c)

20.15

d)

19.4

23.

What equation can be used to solve for x?

a)

Sin(40°)= x/40

b)

Sin(40º)=x/19

c)

Cos(40º)=x/19

d)

Tan(40°)=19/x

24.

Use the Law of Sines to solve for BC

a)

33

b)

24

c)

12

d)

29

25.

Which equation shows how you would use the law of sines to find side c?

a)

$\frac{\sin41}{19}=\frac{\sin\ 75}{c}$

b)

$\frac{\sin\ 64}{19}=\frac{\sin\ 75}{c}$

c)

$\frac{\sin\ 19}{64}=\frac{\sin\ c}{75}$

d)

$\frac{\sin19}{41}=\frac{\sin\ c}{75}$

Law of sines-Cosines

Total questions: 25

Worksheet time: 2hrs 5mins

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