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.
-A fishing boat leaves port on a bearing of $39 ^ { \circ }$ and travels $11.8 \mathrm { mi }$. The boat then turns due east and travels $2.9 \mathrm { mi }$. How far is the fishing boat from port, and what is its bearing from port?
A) $9.7 \mathrm { mi } ; 9.4 ^ { \circ }$
B) $13.8 \mathrm { mi }$; $9.4 ^ { \circ }$
C) $13.8 \mathrm { mi } ; 48.4 ^ { \circ }$
D) $10.2 \mathrm { mi } ; 48.4 ^ { \circ }$

Question

Quizplus · Accepted Answer

The resultant distance can be found using the law of cosines: $c = \sqrt{11.8^2 + 2.9^2 - 2 \times 11.8 \times 2.9 \times \cos(51^\circ)}$, which gives approximately $13.8 \mathrm{mi}$. The bearing is calculated using the law of sines, resulting in approximately $48.4^\circ$.

Use the Parallelogram Rule to Find the Magnitude of the Resultant