# A triangle has sides A, B, and C. Sides A and B are of lengths 2 and 4, respectively, and the angle between A and B is (7pi)/12 . What is the length of side C?

Jun 5, 2018

Length of third side color(brown)(c = 4.91 units

#### Explanation:

a = 2, b = 4, hat C = (7pi)/12, c = ?

Applying the Law of Cosines,

${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos C$

c = sqrt (2^2 + 4^2 - (2 * 2 * 4* cos ((7pi)/12))

Length of third side color(brown)(c = 4.91# units