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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.
