Elevation, depression, bearings
A standard method from Trigonometry: the steps and worked examples.
Steps
- Draw a sketch. Mark the horizontal line first.
- Elevation is measured up from the horizontal; depression down from the horizontal.
- Bearings: true bearings are measured clockwise from north, with three digits (053°). Compass bearings start from N or S and turn towards E or W (N53°E).
- Gradient = vertical rise ÷ horizontal run = tan(inclination). "1 : 4" means rise 1, run 4.
Worked examples
Example 1: A hiker walks 3 km north, then 4 km east. Find the distance and the true bearing of the end point from the start.
Distance = √(3² + 4²) = 5 km. tan θ = 4/3, θ ≈ 53.1°, so the bearing is 053.1° (N53.1°E).
For the whole topic, read Trigonometry: key points, common mistakes and how the DSE tests it.