Distance Between Two Airplanes

Question

Two small airplanes leave the Calgary airport at the same time. The first flies at $225$km/h at a heading of $320^\circ$, while the second flies at $190$km/h at a heading of $70^\circ$. How far apart are they after $2$ hours?

How should I proceed?

Answer 1

Draw it on paper, find their positions using trigonometry and find their distance with the distance formula.

Plane one will be at $(2*225*\cos 320, 2*225*\sin 320)$ and the other will be and $(2*190*\cos 70, 2*190*\sin 70)$.

Their distance will be $\sqrt{ (2*225\cos 320 - 2*190\cos 70)^2 +(2*225\sin 320 - 2*190\sin 70)^2}$

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Or you can use the law of cosines:

$D^2 = (2*225)^2 + (2*190)^2 - 2*225*190*\cos (320 - 70)$.