Chapter 2, Problem 29SE

1. a. For the triangle in the accompanying figure, use trigonometry to show that

   $\begin{array}{l}b\cos \gamma +c\cos \beta =a\\ c\cos \alpha +a\cos \gamma =b\\ a\cos \beta +b\cos \alpha =c\end{array}$

   And then apply Cramer’s rule to show that

   $\cos \alpha =\frac{b^2+c^2-a^2}{2bc}$

2. b. Use Cramer’s rule to obtain similar formulas for cos β and cosγ.