A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 2, respectively, and the angle between A and B is (3pi)/8 . What is the length of side C?

Feb 25, 2018

Length of side color(purple)(c = 5

Explanation:

Given : $a = 7 , b = 2 , \hat{C} = \frac{3 \pi}{8}$

$\textcolor{w h i t e}{a a a a a a a a a a a}$ Applying Law of Cosines

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

c^2 = 7^2 + 2^2 - (2 *7*2*cos((3pi)/8) = 25

$c = 5$