Solve the problem.
-A ship travels $82 \mathrm {~km}$ on a bearing of $30 ^ { \circ }$, and then travels on a bearing of $120 ^ { \circ }$ for $117 \mathrm {~km}$. Find the distance from the starting point to the end of the trip, to the nearest kilometer.
A) $71 \mathrm {~km}$
B) $199 \mathrm {~km}$
C) $143 \mathrm {~km}$
D) $41 \mathrm {~km}$

Question

Quizplus · Accepted Answer

To find the distance from the starting point to the end of the trip, we can use the law of cosines. The angle between the two paths is $90^\circ$ (since $120^\circ - 30^\circ = 90^\circ$). Using the law of cosines: $c^2 = 82^2 + 117^2 - 2 \times 82 \times 117 \times \cos(90^\circ)$. Since $\cos(90^\circ) = 0$, it simplifies to $c^2 = 82^2 + 117^2$. Solving gives $c \approx 143 \mathrm{~km}$.

Solve the Problem 82 km82 \mathrm {~km}82 km On a Bearing Of 30∘30 ^ { \circ }30∘

Solve the Problem $82 \mathrm {~km}$ On a Bearing Of $30 ^ { \circ }$