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.
Example 2 - Solving Triangles
Solve the triangle ABC, given that `A = 35°` and `c = 15.67`.
Angles of Elevation and Depression
In surveying, the angle of elevation is the angle from the horizontal looking up to some object:
The angle of depression is the angle from the horizontal looking down to some object:
Example 3
The angle of elevation of an aeroplane is `23°`. If the aeroplane's altitude is `2500\ "m"`, how far away is it?
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.
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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