Question

A plane is flying at 56 km/h at a bearing of 65 degrees. After flying for 3 hours the plane heading is changed to a bearing of 90 degrees. After flying for a further 1 hour at 56 km/h what is the plane's bearing from its original position

Answer 1

Take north as the y‑axis and east as the x‑axis. For a bearing θ the components are x = d sinθ, y = d cosθ.

First leg: 56 km/h × 3 h = 168 km at 65°:
x1 = 168 sin65° ≈ 152.260 km
y1 = 168 cos65° ≈ 71.000 km

Second leg: 56 km at 90° (east):
x2 = 56 km, y2 = 0

Total: x = 152.260 + 56 = 208.260 km, y = 71.000 km.

Bearing (clockwise from north) = arctan(x / y) = arctan(208.260 / 71.000) ≈ 71.2°.

So the plane's bearing from its original position is about 71.2° (≈ N71.2°E).