A bird flies 4.5 km on a bearing of 075°, how far north and how far…

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The question

Question: a bird goes 4.5 km on a bearing of 075°: how far north and how far east is it from the start?

1 Draw the triangle

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

The path is the long side.

The angle at the start, between north and the path, is the bearing: 75°.

Careful!

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

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

2 How far north

cos is adjacent over hypotenuse.

So the north side is 4.5 times cos 75°: about 1.2 km.

3 How far east

sin is opposite over hypotenuse.

So the east side is 4.5 times sin 75°: about 4.3 km.

4 Check

Let's check with Pythagoras: the two legs squared add up to about 20.25, the path squared.

So it is right!

Let's look back.

First: draw the triangle.

Then: how far north.

Then: how far east.

Last: check.