A plane flies 15 km on a bearing of 300°, how far north and how far…

Step by step

The question

Question: a plane goes 15 km on a bearing of 300°: how far north and how far west is it from the start?

1 Draw the triangle

Go straight north first, then straight west: a right triangle.

The path is the long side.

In the triangle we need the angle at the start, between the path and the north line: 60°.

Careful!

The north side is next to the angle, so it uses cos.

The west side is across from it, so it uses sin.

2 How far north

cos is adjacent over hypotenuse.

So the north side is 15 times cos 60°: about 7.5 km.

3 How far west

sin is opposite over hypotenuse.

So the west side is 15 times sin 60°: about 13.0 km.

4 Check

Let's check with Pythagoras: the two legs squared add up to about 225, the path squared.

So it is right!

Let's look back.

First: draw the triangle.

Then: how far north.

Then: how far west.

Last: check.