Answer
$a= 8.17$ ft
$b= 15.4$ ft
$B=62.0^{\circ}$
Work Step by Step
Step 1: To find $a$, we use the formula $\sin\theta=\frac{a}{c}$.
Step 2: $\sin28.0^{\circ}=\frac{a}{17.4}$
Step 3: $a=17.4\times\sin28.0^{\circ}$
Step 4: Using a calculator, $a\approx8.169$
Step 5: Rounding the answer to three significant degrees, $a\approx8.17$ ft.
Step 6: To find $b$, we use the formula $\cos\theta=\frac{b}{c}$.
Step 7: $\cos28.0^{\circ}=\frac{b}{17.4}$
Step 8: $b=17.4\times\cos28.0^{\circ}$
Step 9: Using a calculator, $b\approx15.36$
Step 10: Rounding the answer to three significant degrees, $b\approx15.4$ ft.
Step 11: As $A+B=90^{\circ}$,
$B=90^{\circ}-28.0^{\circ}$
Step 12: Solving, $B=62.0^{\circ}$.
