Question

2. A boat in calm seas travels in a straight line and ends the trip 16 km west and 50 km north of its original position. Find the direction of the trip to the nearest tenth of a degree.

Answer 1

Answer:

107.8°

Step-by-step explanation:

Here we use the inverse tangent function to determine the angle (direction) of the boat.

"16 km west and 50 km north" places  us in Quadrant III.  One way in which to determine the angle in question, measured from the positive x-axis, is to find the value of arctan 50/16 and then subtract this angle from 180° (or from π radians).

This results in    π - arctan 50/16, or

                          π - 1.26 radians, or 180° - 72.2°, or 107.8°

The boat's direction is 107.8° as measured counterclockwise from the positive x-axis (that is, from ∅ = 0°).