Use the diagram to find the following bearings.

9514 1404 393

  (a) 15°

  (b) 256°

  (c) 133°

  (d) 313°

Step-by-step explanation:

We assume your bearings are to be reported as an angle measured clockwise from north.

A) The given angle is the bearing: 15°.

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B) The bearing can be found by subtracting this angle from 450°:

  450° -194° = 256°

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C) The bearing can be found by adding 90° to the angle shown:

  43° +90° = 133°

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D) The reverse bearing can be found by adding 180°:

  133° +180° = 313°

Additional comment

Angles in Cartesian coordinates are conventionally measured counterclockwise from the +x axis. In that sense, the angle of C could be considered to be -43°.

Bearing angles are reported different ways. One of them is as an angle in the range 0–360°, measured clockwise from north (up, or +y axis). As such, it can be found by subtracting the conventional Cartesian angle from 90°.

When the Cartesian angle is more than 90°, 360° must be added to the difference to bring it back into the desired 0–360° range. Essentially, angles greater than 90° must be subtracted from 90° +360° = 450°.

Reverse bearings are found by adding or subtracting 180°.

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An alternate convention for reporting bearings is as an angle in the range 0–90° east or west from north or south. In this convention, A = N15E, B=S76W, and C=S47E.

Occasionally, you will see the angles B and C reported from east or west: B=W14S; C=E43S. This keeps the angles in the 0–45° range. This is NOT a recommended way to report bearings.

Reverse bearings are found by swapping N/S and E/W. That is, the bearing from A to O is S15W, for example.

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step-by-step explanation: