Bearings, Elevation and Depression

Draw and label the situation before selecting a rule. Bearings are measured clockwise from north and written with three digits. Draw parallel north lines at both locations.

A reverse bearing differs by \(180^\circ\), reduced to \([0^\circ,360^\circ)\). For example, the reverse of \(065^\circ\) is \(245^\circ\).

An elevation angle is measured up from a horizontal line; a depression angle is measured down. Parallel horizontals give equal alternate angles. In the sketch, \(\tan\alpha=\dfrac{h}{d}\).

Add the observer’s eye height when finding a total building height. In a non-right triangle, use the sine or cosine rule after deriving the interior angles from the bearings.

In the next diagram, the directions from \(O\) to \(A\) and \(B\) lie on the same side of north, so the angle between them is \(130^\circ-45^\circ\).