Law of Cosines
See how to use the law of cosines to solve a triangle.
2 examples and their solutions.
Law of Cosines
Formula
a2 = b2 + c2 - 2bccos A
2 sides, 1 angle → 1 side
3 sides → 1 angle.
Example
x2 = 52 + 82 - 2⋅5⋅8⋅cos 60°
= 25 + 64 - 80⋅12 - [1]
= 89 - 40
= 49
x = 7
[1]
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Example
62 = 52 + 42 - 2⋅5⋅4⋅cos θ
36 = 25 + 16 - 40 cos θ
36 = 41 - 40 cos θ
40 cos θ = 5
8 cos θ = 1
cos θ = 18
θ = arccos 18 - [1]
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