Question

The height of the tower is $50$ m when angle of elevation changes from ${45}^0$ to ${30}^0$, the shadow of tower becomes $x$ meters more, find the value of $x$.

• A. $50$
• B. $50\sqrt{30}$
• C. $50(1-\sqrt{3})$
• D. $25$

Answer 1

Answer: (C)

$50(1-\sqrt{3})$

let $BC=y$

In $△ABC$,

$\tan {30}^{\circ }$ $=\frac{50}{y}$

$\frac{1}{\sqrt{3}}=\frac{50}{y}$ $\Rightarrow y=50\sqrt{3}$

In $△ABD$,

$\tan {45}^{\circ }=\frac{50}{y+x}$

$\Rightarrow 1=\frac{50}{y+x}$

$y+x=50\Rightarrow x=50-y$

$x=50-50\sqrt{3}$

$x=50(1-\sqrt{3})$