#### Answer

$\angle A = 51^{\circ}$
$\angle B= 39^{\circ}$
$a =40 ft$

#### Work Step by Step

1. $c = 51ft$ and $b =32 ft$
2. $\angle B = \sin^{-1} \frac{32}{51} = 38.9^{\circ}$
3. $\cos 38.9^{\circ} =\frac{a}{51}$
$a \approx 39.7ft$
4. $\angle A = 180^{\circ} -90^{\circ} -38.9 ^{\circ} = 51.1^{\circ}$
5. Answers in 2 significant figures as given values
$\angle A= 51^{\circ}$ and $\angle B = 39^{\circ}$ and $a = 40ft$