Question

If the angle of elevation of sun is $\theta$ and the length of the shadow of pole of length P is S, then:

• A. $P=Scos\theta$
• B. $P=Ssin\theta$
• C. $P=\frac{S}{cot\theta }$
• D. $P=Scot\theta$

Answer 1

The correct option is C $P=\frac{S}{cot\theta }$

Let $AB=P$ be the height of the pole.

and given that the angle $\theta$ be the angle of elevation from the pole to the length of the shadow.

$\Rightarrow \tan \theta =\frac{P}{S}$

$\therefore P=S\tan \theta =\frac{S}{\cot \theta }$ since $\tan \theta =\frac{1}{\cot \theta }$