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

Mar 25, 2018

color(brown)("Length of side " c = sqrt155.86 ~~ 12.48 " units"

Explanation:

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

Applying Law of Cosines,

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

${c}^{2} = {8}^{2} + {7}^{2} - 2 \cdot 8 \cdot 7 \cdot \cos \left(\frac{5 \pi}{8}\right) \approx 155.86$

color(brown)(c = sqrt155.86 ~~ 12.48 " units"