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Right Triangles

Angles in Standard Position

Sine Law & Ambiguous Case

Cosine Law

Problem Solving

Summary&Test

 

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 UNIT 6 : BASIC TRIGONOMETRY WITH TRIANGLES

 LESSON 4: COSINE LAW HOMEWORK QUESTIONS (Solutions below)

 

 

Quick Summary:

 

1. Given three sides (SSS), use one of the following 3 formulas to find an angle.

Text Box: The Cosine Law:
 

 

 

 


 

 

 

 

 

 

 

2. Given two sides and a contained angle (SAS), use one of the following 3 formulas to find the third side.

 

 

Text Box: The Cosine Law:
 

 

 

 


 

 

These are easy to remember. The first one begins with small a and ends with big A.

The second one begins with small b and ends with big B.

The third one begins with small c and ends with big C.

 

 

Homework Questions: (all measurements in cm. unless otherwise stated. Give answers to the nearest tenth)

(Solutions below).

 

1. In each of the following, determine the missing side.

 

a)

A

 

 

 

c 12.8

 

 

 

B 410

18.7

 

 

b)

 

q

P R

 

 

 

12.3 10.2

 

 

730

Q


 

 

 

 

c) 12.4

D F

430

8.6

d

 

 

E

 

 

 

2. In each of the following, determine the missing angle.

a)

A

 

 

 

13.2 16.3

 

 

 

B C

18.2

 

b)

19.3

M ( P

 

 

 

16.4 13.1

 

 

N


 

 

c) 22.4

D F

 

11.9 18.5

E

 

 

 

 

 

 

 

 

Solutions:

1. In each of the following, determine the missing side.

 

 

a)

A

 

 

 

c 12.8

 

 

 

B 410 C

18.7

 

Solution:

This is the SAS case. Use the cosine law for side c.

 

 

 

 

b)

 

q

P R

 

 

 

12.3 10.2

 

 

730

Q


Solution:

This is the SAS case. Use the cosine law for side q.

 

 

c) 12.4

D F

430

8.6

d

 

E

 

Solution:

This is the SAS case. Use the cosine law for side d.

 

 

 

 

2. In each of the following, determine the missing angle.

a)

A

 

 

 

13.2 16.3

 

 

 

B C

18.2

 

Solution:

This is the SSS case. Use the cosine law for angle B.

 

 

 

b)

19.3

M ( P

 

 

 

16.4 13.1

 

 

N

 

Solution:

This is the SSS case. Use the cosine law for angle P.


 

 

 

 

c) 22.4

D F

 

11.9 18.5

E

 

 

Solution:

This is the SSS case. Use the cosine law for angle E.


 

3. Solve each of the triangles below. Include a sketch.

 

 

F

 

 

 

10.1 d

 

 

 

D 610 E

11.7

 

Solution:

This is the SAS case. Use the cosine law for side d.

 

 

 

 

9.5

P R

 

 

 

11.4 7.1

 

 

Q


Solution:

This is the SSS case. Use the cosine law for any angle, say angle P.

 

 

 

 

A

 

 

 

6.8 13.2

 

 

 

B C

10.1

 

Solution:

This is the SSS case. Use the cosine law for any angle, say angle A.

 

 

 

 

e

D F

13.3

15.4

113.20

 

E

Solution:

This is the SAS case. Use the cosine law for side e.

 

 

 

 

 

 

 

 

A

 

 

 

21.5 35.3

 

 

 

B C

18.7

 

Solution:

This is the SSS case. Use the cosine law for any angle, say angle A.

 

 

 

 

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