9514 1404 393
Answer:
(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°
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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.
