Question

The angle of elevation of the Sun if the shadow of a 7 m long pole is $7\sqrt{3}$ m, is

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

Let AB be the pole and BC be its shadow. Let the angle of elevation of the Sun be $\alpha .$
Then, $\angle BCA=\alpha ,and\angle ABC={90}^{\circ }$.
In the right-angled $\Delta ABC$,
$tan\alpha =\frac{AB}{BC}$
$\Rightarrow tan\alpha =\frac{7}{7\sqrt{3}}(BecauseAB=7mandBC=7\sqrt{3}m)$
$\Rightarrow tan\alpha =\frac{1}{\sqrt{3}}=tan{30}^{\circ }$
$\Rightarrow \alpha ={30}^{\circ }$
Hence, the correct answer is option (2).