Home Right Triangles Angles in Standard Position Sine Law & Ambiguous Case Cosine Law Problem Solving Summary&Test

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.

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.

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.