A plane flies along a straight line path after taking off, and it ends up 190 km farther east and 80.0 km farther north, relative to where it started. What is the plane's displacement?

You can use the Pythagorean theorem to solve this problem.

Along the x-axis, displacement is 190km

Along the y-axis, displacement is 80km

x² + y² = r²

[solve for r]

r = √ ((190) ² + (80) ²)

r = 206.16km

tanθ = (y/x)

[solve for θ]

θ = tan⁻¹ (80/190)

θ = 22.83°

Therefore, displacement of plane is 206.16 km 22.83° north of east

or

206.16 km 67.17° east of north.