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?

Jun 18, 2018

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

Explanation:

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

$a = 4 , b = 7 , \hat{C} = \frac{5 \pi}{8}$

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"