# 4. The Right Triangle and Applications

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

Find h.

### Example 2 - Solving Triangles

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

Continues below

## 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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