Answer
$c = 20.5 ft$
$\angle A= 37.7 ^{\circ}$
$\angle B =52.3 ^{\circ}$
Work Step by Step
1. $a = 12.5 ft$; $b = 16.2 ft$
$\angle C = 90^{\circ}$
2. $\tan A = \frac{a}{b}= \frac{12.5}{16.2}$
$\angle A = \tan^{-1} (0.771604383) \approx 37.7^{\circ}$
3. $\angle A+ \angle B = 90^{\circ}$
$ \angle B = 90^{\circ} -37.7^{\circ} = 52.3^{\circ}$
4. Pythagoream theorem
$c^2 = 12.5^2 + 16.2^2$
$c = \sqrt {156.25+262.44}$
$c = 20.5 ft$ consider only positive root, as length always positive in trigonometry
