Answer
$b=6.61$ m
$c=14.3$ m
$B=27.5^{\circ}$
Work Step by Step
Step 1: To find $b$, we use the formula $\tan\theta=\frac{a}{b}$.
Step 2: $\tan62.5^{\circ}=\frac{12.7}{b}$
Step 3: $b=\frac{12.7}{\tan62.5^{\circ}}$
Step 4: Using a calculator, $b\approx6.611$
Step 5: Rounding the answer to three significant degrees, $b\approx6.61$ m.
Step 6: To find $c$, we use the formula $\sin\theta=\frac{a}{c}$.
Step 7: $\sin62.5^{\circ}=\frac{12.7}{c}$
Step 8: $c=\frac{12.7}{\sin62.5^{\circ}}$
Step 9: Using a calculator, $c\approx14.32$
Step 10: Rounding the answer to three significant degrees, $c\approx14.3$ m.
Step 11: As $A+B=90^{\circ}$,
$B=90^{\circ}-62.5^{\circ}$
Step 12: Solving, $B=27.5^{\circ}$.
