Question

The length of shadow of a tower on the plane ground is $\sqrt{3}$ times the height of the tower. The angle of elevation of sun is:

• A. ${45}^0$
• B. ${30}^0$
• C. ${60}^0$
• D. ${90}^0$

Answer 1

Answer: (B)

${30}^0$

Let the height of the tower be h meter.

Then the length of the tower be $\sqrt{3}h$ meter

$\therefore$ In $△ABC$

$\Rightarrow tan\theta =\frac{AB}{BC}$

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

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

$\Rightarrow tan\theta =tan{30}^{\circ }$ [$\because tan{30}^{\circ }=\frac{1}{\sqrt{3}}$]

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