SL 3.3—Applications of trigonometry

Applied trigonometry converts bearings, elevation, depression and written spatial relationships into right or non-right triangles that can be solved with Pythagoras, trigonometric ratios, the sine rule or the cosine rule.

Draw the north line for bearings, mark horizontal sight lines for elevation or depression, label known sides and angles, and decide whether triangles share a length. Keep bearings as three-figure clockwise angles from north.

Example

A point is 80 m horizontally from a tower and the angle of elevation to the top is $32^\circ$. Then $\tan32^\circ=h/80$, so $h=80\tan32^\circ\approx50.0$ m. State whether eye height must be added in the actual context.

Do not take a bearing from the wrong north line or use an angle of depression as an angle inside a triangle without transferring it through parallel horizontals. A labelled diagram is part of the reasoning.