Step by step
The question
Question: A is 8 km north and 6 km west of B: find the distance and the bearing of A from B.
1 Distance
8 km north, then 6 km west: the two short sides of a right triangle.
Pythagoras: 8 squared plus 6 squared is 100.
The square root is 10 km.
BA = √(8² + 6²) = √100 = 10 km
2 Angle from the north-south line
At B, the west side is across from the angle and the north side is next to it: tan.
tan to the minus 1 gives about 36.9°.
angle = tan⁻¹(68) ≈ 36.9°
Careful!
The angle we found is from the north line.
A bearing is measured from north, turning clockwise.
Careful: a bearing is always from NORTH, clockwise
3 Bearing
From north, clockwise: 323.1°.
bearing = 360° − 36.9° = 323.1°
4 Check
Let's check: the distance times cos of the angle gives back about 8 km north.
So it is right!
10 × cos 36.9° ≈ 8.0 = 8 km north
Let's look back.
First: distance.
Then: angle from the north-south line.
Then: bearing.
Last: check.
Answer
bearing = 360° − 36.9° = 323.1°