Chapter 1, Problem 18P

18. In the triangle shown a =27 in., b 43 in., c=57 in. Define a, b, and c as variables, and then:

(a) Calculate the angles $\alpha$ , $\beta$ ,and $\gamma$ by substituting the variables in the law of cosines.

 (Law of cosines: $c^2=a^2+b^2-2abcos\gamma$ )

(b)Verify the law of tangents by substituting the results into the right and left sides of:

law of tangents: $\frac{b-c}{b+c}=\frac{\tan \left[\frac{1}{2}(\beta -\gamma )\right]}{\tan \left[\frac{1}{2}(\beta +\gamma )\right]}$