Step by step
The question
Question: A is 7 km north and 3 km east of B: find the distance and the bearing of A from B.
1 Distance
7 km north, then 3 km east: the two short sides of a right triangle.
Pythagoras: 7 squared plus 3 squared is 58.
The square root is about 7.6 km.
BA = √(7² + 3²) = √58 ≈ 7.6 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 23.2°.
angle = tan⁻¹(37) ≈ 23.2°
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, 023.2°.
bearing = 023.2°
4 Check
Let's check: the distance times cos of the angle gives back about 7 km north.
So it is right!
7.6 × cos 23.2° ≈ 7.0 = 7 km north
Let's look back.
First: distance.
Then: angle from the north-south line.
Then: bearing.
Last: check.
Answer
bearing = 023.2°