Question

The length of the shadow of a person is x when the angle of elevation of the sun is ${45}^0$. If the length of the shadow increased by $(\sqrt{3}-1)x$ then the angle of elevation becomes

• A. ${15}^0$
• B. ${18}^0$
• C. ${25}^0$
• D. ${30}^0$

Answer 1

The correct option is D ${30}^0$

Let $AB$ be the height of the person, $AC$ and $AD$ be his shadows at two instants.

$AC=x$

$AD=AC+CD=x+(\sqrt{3}-1)x$$=\sqrt{3}x$

and $\angle ACB={45}^0$

$\frac{AB}{AC}=\tan {45}^0=1\Rightarrow AB=AC=x$

$\tan \theta =\frac{AB}{AD}=\frac{x}{\sqrt{3x}}=\frac{1}{\sqrt{3}}$

$\Rightarrow \theta ={30}^0$