Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to
one decimal place.
-Starting at point $\mathrm { A }$, a ship sails $57 \mathrm {~km}$ on a bearing of $186 ^ { \circ }$, then turns and sails $35 \mathrm {~km}$ on a bearing of $303 ^ { \circ }$. Find the distance of the ship from point $\mathrm { A }$.
A) $92 \mathrm {~km}$
B) $52 \mathrm {~km}$
C) $- 5 \mathrm {~km}$
D) $87 \mathrm {~km}$

Question

Quizplus · Accepted Answer

To find the distance of the ship from point A, we can use the law of cosines or vector addition. The bearings can be converted to angles from the north direction: the first leg is $186^\circ - 180^\circ = 6^\circ$ to the west of south, and the second leg is $303^\circ - 270^\circ = 33^\circ$ to the north of west. The angle between the two vectors is $180^\circ - 6^\circ + 33^\circ = 207^\circ$. Using the law of cosines: $d = \sqrt{57^2 + 35^2 - 2 \cdot 57 \cdot 35 \cdot \cos(207^\circ)}$, which gives a distance of approximately $52 \mathrm{~km}$.

Use the Parallelogram Rule to Find the Magnitude of the Resultant