Answer
$a=571$ m
$b=777$ m
$B=53^{\circ}40'$
Work Step by Step
Step 1: To find $a$, we use the formula $\sin\theta=\frac{a}{c}$.
Step 2: $\sin36^{\circ}20'=\frac{a}{964}$
Step 3: Converting the angle to decimal degrees;
$36^{\circ}20'=36\frac{20}{60}^{\circ}=36.3^{\circ}$
Step 4: $a=964\times\sin36.3^{\circ}$
Step 5: Using a calculator, $a\approx570.7$
Step 6: Rounding the answer to three significant degrees, $a\approx571$ m.
Step 7: To find $b$, we use the formula $\cos\theta=\frac{b}{c}$.
Step 8: $\cos36.3^{\circ}=\frac{b}{964}$
Step 9: $b=964\times\cos36.3^{\circ}$
Step 10: Using a calculator, $b\approx776.9$
Step 11: Rounding the answer to three significant degrees, $b\approx777$ m.
Step 12: As $A+B=90^{\circ}$,
$B=90^{\circ}-36^{\circ}20'$
Step 13: Solving, $B=53^{\circ}40'$.
