Question:
An observer 1.5 m tall is 20.5 m away from a tower 22 m high. Determine the angle of elevation of the top of the tower from the eye of the observer.
Solution:
Let the angle of elevation of the top of the tower from the eve of the observe is $\theta$
Given that, $\quad A B=22 \mathrm{~m}, P Q=1.5 \mathrm{~m}=M B$
and $\quad Q B=P M=20.5 \mathrm{~m}$
$\Rightarrow \quad A M=A B-M B$
$=22-1.5=20.5 \mathrm{~m}$
Now, in $\triangle A P M, \quad \tan \theta=\frac{A M}{P M}=\frac{20.5}{20.5}=1$
$m \quad \tan A=\tan 45^{\circ}$
$\therefore \quad \theta=45^{\circ}$
which may be either positive or negative.Hence, required angle of elevation of the top of the tower from the eye of the observer is 45°.