Answer
$a\approx 310.8 ft$
$b \approx 230.8 ft$
$\angle B = 36^{\circ} 36'$
Work Step by Step
1.Given $A = 53^{\circ} 24' = 53. 4 ^{\circ}$ (converted to degrees for further calcualation) and$c = 387.1 ft$
2. Use sine to find $a$
$\sin 53.4^{\circ} = \frac{a}{387.1}$ => $a\approx310.8 ft$
3. Use cosine to find side $b$
$\cos 53.4^{\circ} = \frac{b}{387.1}$ => $b \approx 230.8 ft$
4. Angles in a triable add up to 180 degrees, therefore
$\angle B = 180^{\circ} -90^{\circ} -53.4^{\circ} = 36.6^{\circ}\approx 36^{\circ} 36'$ converted into minutes with 4 significant figures, corresponding given values
