Chapter 1, Problem 17P

In the triangle shown a = 5 in., b = 7 in., and $\gamma$ = 25°. Define a, b,and $\gamma$ as variables, and then:

1. Calculate the length of c by substituting the variables in the Law of Cosines.

(Law of Cosines: c²= a²+ b²- 2abcos $\gamma$)

Calculate the angles $\alpha$ and $\beta$ (in degrees) using the Law' of Sines.

Verify the Law of Tangents by substituting the results from part (b) into the right and left sides of the equation.

$\text{Law}\text{of}\text{tangents:}\frac{a-b}{a+b}=\frac{\tan \left[\frac{1}{2}\left(\text{α}-\text{β}\right)\right]}{\left[\frac{1}{2}\left(\text{α}+\text{β}\right)\right]}$