Question

A triangle has sides A, B, and C. Sides A and B are of lengths `4` and `7`, respectively, and the angle between A and B is `(5pi)/8`. What is the length of side C?

Answer 1

`c = sqrt(4^2 + 7^2 - (2 * 4 * 7 * cos ((5pi)/8))) ~~ color(crimson)(9.3 " units"`

Explanation:

`c^2 = a^2 + b^2 - 2ab cos C`

`a = 4, b = 7, hat C = (5pi)/8`

`c^2 = 4^2 + 7^2 - (2 * 4 * 7 * cos ((5pi)/8)`

`c = sqrt(4^2 + 7^2 - (2 * 4 * 7 * cos ((5pi)/8))) ~~ color(crimson)(9.3 " units"`