Answer
$a=39.1$ in
$c=134$ in
$A=17.0^{\circ}$
Work Step by Step
Step 1: To find $a$, we use the formula $\tan\theta=\frac{b}{a}$.
Step 2: $\tan73.0^{\circ}=\frac{128}{a}$
Step 3: $a=\frac{128}{\tan73.0^{\circ}}$
Step 4: Using a calculator, $a\approx39.13$
Step 5: Rounding the answer to three significant degrees, $a\approx39.1$ in.
Step 6: To find $c$, we use the formula $\sin\theta=\frac{b}{c}$.
Step 7: $\sin73.0^{\circ}=\frac{128}{c}$
Step 8: $c=\frac{128}{\sin73.0^{\circ}}$
Step 9: Using a calculator, $c\approx133.8$
Step 10: Rounding the answer to three significant degrees, $c\approx134$ in.
Step 11: As $A+B=90^{\circ}$,
$A=90^{\circ}-73.0^{\circ}$
Step 12: Solving, $A=17.0^{\circ}$.
