Math CentralQuandaries & Queries


Question from sam, a student:

A passenger on a ship sailing north at 5.0 mph noticed that at noon a radio tower on land was due east of the ship. At 1:30 p.m., the bearing of the tower from the ship was S35degreesE. How far was the ship from the tower at 1:30 p.m.

Hi Sam. How far north has the ship traveled in that time?

Draw a right triangle with the corners at these locations:
a) The position of the ship at noon.
b) The position of the ship at 1.30pm.
c) The position of the tower.

It is okay to be approximate, but remember that north and east are perpendicular directions.

Now identify the bearing angle on your diagram. How does that relate to one of the internal angles of the triangle? You should be able to write the value of one of the internal angles of the triangle.

Whenever you have a right triangle where you know the length of one side (the distance the ship has traveled north) and one interior angle, you can calculate any other side length of the triangle. In this case you want to know the hypotenuse.

So what trig function can you use to find the length of the hypotenuse when you know that angle and that side?

Hope this helps,
Stephen La Rocque.

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