Answer
$a=32.38$ m
$c=50.66$ m
$B=50.28^{\circ}$
Work Step by Step
Step 1: To find $a$, we use the formula $\tan\theta=\frac{a}{b}$.
Step 2: $\tan39.72^{\circ}=\frac{a}{38.97}$
Step 3: $a=38.97\times\tan39.72^{\circ}$
Step 4: Using a calculator, $a\approx32.376$
Step 5: Rounding the answer to four significant degrees, $a\approx32.38$ m.
Step 6: To find $c$, we use the formula $\cos\theta=\frac{b}{c}$.
Step 7: $\cos39.72^{\circ}=\frac{38.97}{c}$
Step 8: $c=\frac{38.97}{\cos39.72}$
Step 9: Using a calculator, $c\approx50.664$
Step 10: Rounding the answer to four significant degrees, $b\approx50.66$ m.
Step 11: As $A+B=90^{\circ}$,
$B=90^{\circ}-39.72^{\circ}$
Step 12: Solving, $B=50.28^{\circ}$.
