Using a calculator, solve the following problems. Round your answers to the nearest tenth.
-A ship leaves port with a bearing of $\mathrm { N } 72 ^ { \circ } \mathrm { W }$. After traveling 20 miles, the ship then turns $90 ^ { \circ }$ and travels on a bearing of $\mathrm { S } 18 ^ { \circ } \mathrm { W }$ for 17 miles. At that time, what is the bearing of the ship from port?
A) $\mathrm { N } \mathrm {} 112.4 ^ { \circ } \mathrm { W }$
B) $\mathrm { N } \mathrm {} 40.4 ^ { \circ } \mathrm { W }$
C) $\mathrm { N } 58.4 ^ { \circ } \mathrm { W }$
D) N $31.6 ^ { \circ } \mathrm { W }$

Question

Quizplus · Accepted Answer

The correct answer is A because the ship travels 20 miles on a bearing of N 72° W, and then turns 90° and travels 17 miles on a bearing of S 18° W. The total distance traveled is 20 + 17 = 37 miles. The bearing of the ship from port is the angle between the line from port to the ship's starting point and the line from port to the ship's final position. This angle can be found using the arctangent function:```bearing = arctan(opposite / adjacent)```In this case, the opposite side is the distance traveled on the second leg (17 miles), and the adjacent side is the distance traveled on the first leg (20 miles). So, the bearing is:```bearing = arctan(17 / 20) = 40.4°```Since the ship is traveling west, the bearing is N 40.4° W.

Using a Calculator, Solve the Following Problems N72∘W\mathrm { N } 72 ^ { \circ } \mathrm { W }N72∘W

Using a Calculator, Solve the Following Problems $\mathrm { N } 72 ^ { \circ } \mathrm { W }$