Solve the problem.
-A ship travels $89 \mathrm {~km}$ on a bearing of $25 ^ { \circ }$, and then travels on a bearing of $115 ^ { \circ }$ for $115 \mathrm {~km}$. Find the distance from the starting point to the end of the trip, to the nearest kilometer.
A) $38 \mathrm {~km}$
B) $204 \mathrm {~km}$
C) $145 \mathrm {~km}$
D) $81 \mathrm {~km}$

Question

Quizplus · Accepted Answer

Using the law of cosines in the triangle formed by the ship's path, the angle between the two paths is $90^\circ$. The distance is calculated as $\sqrt{89^2 + 115^2 - 2 \times 89 \times 115 \times \cos(90^\circ)}$, which simplifies to approximately $145 \mathrm{~km}$.

Solve the Problem 89 km89 \mathrm {~km}89 km On a Bearing Of 25∘25 ^ { \circ }25∘

Solve the Problem $89 \mathrm {~km}$ On a Bearing Of $25 ^ { \circ }$