Solve the problem.
-A boat sails for 5 hours at $20 \mathrm { mph }$ in a direction $173.52 ^ { \circ }$. How far south has it sailed (to the nearest mile)?
A) $97 \mathrm { mi }$
B) $95 \mathrm { mi }$
C) $101 \mathrm { mi }$
D) $99 \mathrm { mi }$

Question

Quizplus · Accepted Answer

The boat's southward distance can be calculated using the sine of the angle from the north direction and the total distance traveled. The total distance is $5 \times 20 = 100$ miles. The angle from the north is $173.52^\circ - 180^\circ = -6.48^\circ$, but since we're interested in the absolute value for distance, we use $6.48^\circ$. The southward distance is $100 \times \sin(6.48^\circ) \approx 99$ miles, rounding to the nearest mile.

Solve the Problem 20mph20 \mathrm { mph }20mph In a Direction 173.52∘173.52 ^ { \circ }173.52∘

Solve the Problem $20 \mathrm { mph }$ In a Direction $173.52 ^ { \circ }$