Law of Cosines

Law of Cosines

CONCEPTS

Law of Cosines

• c² = a² + b² – 2ab cos C (a, b, c are sides, C is an angle)

• Either 2 sides and 1 angle (that is opposite of the side that is requested) is given or 3 sides is given.

• This can be used on any triangle (not just right triangles)

PRACTICE PROBLEMS

Question 1 Find the angle θ (see figure below)

-- Answer -- θ = 24.4°

Given 3 sides => use law of cosines

42.7² = 95.1² + 70.0² - 2 * 95.1 * 70.0 * cos θ

-12120.72 = -2 * 95.1 * 70.0 * cos θ

0.91037 = cos θ

θ = 24.4°

Question 2 Find the 3rd side (see figure below)

-- Answer -- c = 8.1

Given 2 sides and 1 angle => use law of cosines

c² = 16² + 7² - 2 * 16 * 7 * cos 36°

c = 8.1

ACT PRACTICE PROBLEMS

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