#### Answer

$b=35.6$ ft
$c=45.3$ ft
$A=38.3^{\circ}$

#### Work Step by Step

Step 1: To find $b$, we use the formula $\tan\theta=\frac{b}{a}$.
Step 2: $\tan51.7^{\circ}=\frac{b}{28.1}$
Step 3: $b=\tan51.7^{\circ}\times28.1$
Step 4: Using a calculator, $b\approx35.58$
Step 5: Rounding the answer to three significant degrees, $b\approx35.6$ ft.
Step 6: To find $c$, we use the formula $\cos\theta=\frac{a}{c}$.
Step 7: $\cos51.7^{\circ}=\frac{28.1}{c}$
Step 8: $c=\frac{28.1}{\cos51.7^{\circ}}$
Step 9: Using a calculator, $c\approx45.34$
Step 10: Rounding the answer to three significant degrees, $c\approx45.3$ ft.
Step 11: As $A+B=90^{\circ}$,
$A=90^{\circ}-51.7^{\circ}$
Step 12: Solving, $A=38.3^{\circ}$.