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.
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°.
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