Step by step
The question
Question: A is 6 km north and 8 km east of B: find the distance and the bearing of A from B.
1 Distance
6 km north, then 8 km east: the two short sides of a right triangle.
Pythagoras: 6 squared plus 8 squared is 100.
The square root is 10 km.
BA = √(6² + 8²) = √100 = 10 km
2 Angle from the north-south line
At B, the east side is across from the angle and the north side is next to it: tan.
tan to the minus 1 gives about 53.1°.
angle = tan⁻¹(86) ≈ 53.1°
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
North, then turning clockwise to the east side: the bearing is the angle itself, 053.1°.
bearing = 053.1°
4 Check
Let's check: the distance times cos of the angle gives back about 6 km north.
So it is right!
10 × cos 53.1° ≈ 6.0 = 6 km north
Let's look back.
First: distance.
Then: angle from the north-south line.
Then: bearing.
Last: check.
Answer
bearing = 053.1°