Question

An observer 1.5 metres tall is 20.5 metres away from a tower 22 metres high. Determine the angle of elevation of the top of the tower from the eye of the observer.

Options

• 30°

• 45°

• 60°

• 90°

Answer 1

45°

Explanation:

Let the angle of elevation of the tower from the eye of the observer be `theta`.

Given that:

AB = 22m, PQ = 1.5m = MB

QB = PM = 20.5m

AM = AB - MB = 22 - 1.5 = 20.5m

Now in triangle APM

`"tan" theta = "AM"/"PM"`

`"tan" theta = 20.5/20.5`

`"tan" theta = 1`

`theta = 45^circ`