Chapter 1, Problem 16P

In the triangle shown $a=5.3\text{in}\text{.,}\gamma \text{=}\text{42°,}\text{and}b=6$ in. Define a, $\gamma$,and bas variables, and then:

(a) Calculate the length bby using the Law of Cosines.

$\left(\text{Law}\text{of}\text{Cosines:}{c}^2=a^2+b^2-2ab\cos \gamma \right)$

(b) Calculate the angles $\beta$ and $\gamma$ (in degrees) using the Law of Cosines.

(c) Check that the sum of the angles is 180°.