4. The Right Triangle and Applications

Many problems involve right triangles. We often need to use the trigonometric ratios to solve such problems.

Example 1 - Finding the Height

Find h.

Triangle with unknown height h

Example 2 - Solving Triangles

Solve the triangle ABC, given that `A = 35°` and `c = 15.67`.

Triangle sides a,b,c and angles A,B,C

Angles of Elevation and Depression

In surveying, the angle of elevation is the angle from the horizontal looking up to some object:

Angle of elevation

The angle of depression is the angle from the horizontal looking down to some object:

Angle of depression

Example 3

The angle of elevation of an aeroplane is `23°`. If the aeroplane's altitude is `2500\ "m"`, how far away is it?

Cessna trigonometry application

Example 4

You can walk across the Sydney Harbour Bridge and take a photo of the Opera House from about the same height as top of the highest sail.

opera house

This photo was taken from a point about `500\ "m"` horizontally from the Opera House and we observe the waterline below the highest sail as having an angle of depression of `8°`. How high above sea level is the highest sail of the Opera House?

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