A triangle has sides A, B, and C. Sides A and B are of lengths 5 and 7, respectively, and the angle between A and B is (3pi)/8 . What is the length of side C?

May 22, 2016

$C = 10.04$

Explanation:

Cosine law states that if two sides $A$ and $B$ and included angle $\gamma$ is given than third side $C$ is

$C = \sqrt{{A}^{2} + {B}^{2} + 2 A B \cos \gamma}$

Here $A = 5$, $B = 7$ and included angle is $\frac{3 \pi}{8}$

Hence C=sqrt(5^2+7^2+2xx5xx7xxcos((3pi)/8)

= sqrt(25+49+70xx0.3827

= $\sqrt{74 + 26.789} = \sqrt{100.789} = 10.04$