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Right Triangles

Angles in Standard Position

Sine Law & Ambiguous Case

Cosine Law

Problem Solving

Summary&Test

 

jdsmathnotes

 

 


 UNIT 6 : BASIC TRIGONOMETRY WITH TRIANGLES

 LESSON 4: COSINE LAW

 

The Cosine Law:

The cosine law is also used to solve oblique triangles, that is triangles which are not right angled.

It is used in the following two situations.

 

1. 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.

 

The above formulas allow us to find the third side of the given triangle.

 

Example 1:

 

A

 

 

 

12.9 b

 

 

 

B 52o C

18.6

 

Solution:

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

 

 

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

Text Box: The Cosine Law:
 

 

 

 


 

 

 

 

 

Example 2:

 

26.4

P R

 

 

 

22.1 15.8

 

 

Q


Solution:

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

 

 

 

Example 3:

 

 

C

 

 

 

11.7

 

 

A 1050 B

9.4

 

Solution:

This is the SAS case with < A obtuse. Use the cosine law to find side a.

 

 

 

 

Example 4:

 

 

36.4

P R

 

 

 

22.6 19.8

 

 

Q


Solution:

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

 

 

 

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