Question

If a tower casts a shadow $\sqrt{3}$ times of its height on the ground, then the angle of elevation of the Sun is

• A. 30º
• B. 45º
• C. 60º
• D. 15º

Answer 1

The correct option is A 30º

Let AB be the tower of height h and BC be its shadow.
Therefore, the length of the shadow casted by tower on the ground is $\sqrt{3}h$.
Let θ be the angle of elevation of the Sun.
$In\Delta ABC,$
$\tan \theta =\frac{AB}{BC}$
$\Rightarrow \tan \theta =\frac{h}{\sqrt{3}h}=\frac{1}{\sqrt{3}}$
$\Rightarrow tan\theta =tan{30}^o$
$\Rightarrow \theta ={30}^o$
Hence, the correct answer is option (a).