Question

A phone receives signals from a transmitter that is 13 km west and 21 km south of it.

What is the bearing from the phone to the transmitter?
Give your answer to the nearest degree.

Answer 1

212°

Explanation:

You want the bearing to a transmitter located 13 km west and 21 km south of a given location.

Bearing

The bearing angle is measured clockwise from north. It is a 3rd-quadrant angle, so lies between 180° and 270°.

One way to find the angle is to use the arctangent function:

bearing = 270° -arctan(21/13) = 270° -58° = 212°

For this formula, the reference angle is the angle of the transmitter relative to the -x axis.

The bearing of the transmitter is 212°.

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Additional comment

The attached calculator display shows computation of the angle using (N, E) coordinates, written as a complex number. Then the calculator's polar conversion function works to translate that to a bearing angle measured clockwise from north. That conversion renders angles to the range -180° to +180°, so we need to add 360° to make the negative value positive.

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