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°).
