Question

The height of the tower is 100 m. When the angle of elevation of the sun changes from ${30}^{\circ }to{45}^{\circ }$, the shadow of the tower becomes x metres less. The value of x is :

• A. $100m$
• B. $100\sqrt{3}m$
• C. $100(\sqrt{3}-1)m$
• D. $\frac{100}{\sqrt{3}}m$

Answer 1

The correct option is C

$100(\sqrt{3}-1)m$

In $\Delta ABC$ , $tan{45}^{\circ }=\frac{AB}{BC}$

$\Rightarrow AB=BC=100(tan{45}^{\circ }=1)$

In $\Delta ABD,tan{30}^{\circ }=\frac{100}{(100+x)}\Rightarrow \frac{1}{\sqrt{3}}=\frac{100}{(100+x)}\Rightarrow 100+x=100\sqrt{3}\Rightarrow x=100(\sqrt{3}-1)m$