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Cosine Law

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Summary&Test

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.

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

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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