#### Answer

γ = 55.1°

#### Work Step by Step

Using theorem 11.4.2
Law of sines:
$\frac{sine α}{a}$ = $\frac{sine γ}{b}$
$\frac{sine 80°}{12 in}$ = $\frac{sine γ}{10 in}$
sine γ = $\frac{sine 80°}{12 in}$ * 10 in
sine γ = 0.8206
γ = $sin^{-1}$(0.8206)
γ = 55.1°