Answer
$a=70.7$ cm
$c=80.9$ cm
$B=29.0^{\circ}$
Work Step by Step
Step 1: To find $a$, we use the formula $\tan\theta=\frac{a}{b}$.
Step 2: $\tan61.0^{\circ}=\frac{a}{39.2}$
Step 3: $a=\tan61.0^{\circ}\times39.2$
Step 4: Using a calculator, $a\approx70.72$
Step 5: Rounding the answer to three significant degrees, $a\approx70.7$ cm.
Step 6: To find $c$, we use the formula $\cos\theta=\frac{b}{c}$.
Step 7: $\cos61.0^{\circ}=\frac{39.2}{c}$
Step 8: $c=\frac{39.2}{\cos61.0^{\circ}}$
Step 9: Using a calculator, $c\approx80.86$
Step 10: Rounding the answer to three significant degrees, $c\approx80.9$ cm.
Step 11: As $A+B=90^{\circ}$,
$B=90^{\circ}-61.0^{\circ}$
Step 12: Solving, $B=29.0^{\circ}$.
