If the length of the shadow of a tower is

Question:

If the length of the shadow of a tower is $\sqrt{3}$ times its height then the angle of elevation of the sun is

(a) 45°
(b) 30°
(c) 60°
(d) 90°

Solution:

(b) 30°

Let $A B$ be the pole and $B C$ be its shadow.

Let $A B=h$ and $B C=x$ such that $x=\sqrt{3} h$ (given) and $\theta$ be the angle of elevation.

From $\triangle A B C$, we have:

$\frac{A B}{B C}=\tan \theta$

$\Rightarrow \frac{h}{x}=\frac{h}{\sqrt{3} h}=\tan \theta$

$\Rightarrow \tan \theta=\frac{1}{\sqrt{3}}$

$\Rightarrow \theta=30^{\circ}$

Hence, the angle of elevation is $30^{\circ}$.

 

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