Question

A triangle has sides A, B, and C. Sides A and B are of lengths `6` and `5`, respectively, and the angle between A and B is `(7pi)/12`. What is the length of side C?

Answer 1

C = `sqrt( 61 + 15sqrt2(sqrt3-1)`

Explanation:

#C^2 = A^2 + B^2 - 2A B cos (7pi/12) = 61-60 cos(7pi/12)# `cos(7pi/12) = cos (4pi/12+3pi/12) = cos (pi/4+pi/3)`