Question

A plane flies along a straight line path after taking off, and it ends up 90.0 km farther

east and 200.0 km farther north, relative to where it started. In what direction did it
fly on the straight line path?
27° north of east
45 ° north of east
24° north of east
66° north of east

Answer 1

66° north of east

Step-by-step explanation:

The flight path can be modeled as the hypotenuse of a right triangle. When the direction angle is measured north of east, the distance north is opposite the angle in the right triangle, and the distance east is adjacent. The relevant trig relation is ...

Tan = Opposite/Adjacent

__

setup

Using the given distances, the angle θ north of east will be ...

tan(θ) = (200.0 km)/(90.0 km) = 20/9

solution

The measure of the angle is found using the inverse tangent function.

θ = arctan(20/9) ≈ 65.7723°

The straight line path is in the direction 66° north of east.