1. Law of Cosines C a b A B c

2. : -1≤ cosØ ≤1 when 0˚≤ Ø ≤180˚
: To use the Law of Cosines, you must know 3 things, one of which is a side.
: If you know an angle, start by finding its corresponding side.
: Using the Law of Cosines will result in only 1 solution because there is only 1 angle between 0˚ and 180˚ with the given cosine.

3. : We find C by taking 180-(sum of A+B). Ex:
Solve each triangle. Round angle measures to the nearest
minute & side measures to the nearest tenth.
1. a=1.5, b=2.3, c=1.9
Since we know all 3 sides, we can pick any side to start with:
Now we can use either Law of Sines or Law of Cosines. Recall that Law of Sines may result in more than 1 answer.
A= a=1.5
B= b=2.3
C= c=1.9
40˚28’
: We find C by taking
180-(sum of A+B).
84˚16’
55˚16’

4. : We find C by taking 180-(sum of A+B). Ex:
Solve each triangle. Round angle measures to the nearest
minute & side measures to the nearest tenth.
2. b=40, c=45, A=51˚
Since we know 2 sides and angle A, find a:
Now we can use either Law of Sines or Law of Cosines. Recall that Law of Sines may result in more than 1 answer.
A= 51˚ a=
B= b=40
C= c=45
36.9
: We find C by taking
180-(sum of A+B).
57˚27’
71˚33’