Question

The length of the shadow of a tower standing on level ground is found to be 2x metres longer when the sun's elevation is ${30}^{\circ }$ than when it was ${45}^{\circ }$. The height of the tower is

(a) $\left(2\sqrt{3}x\right)m$

(b) $\left(3\sqrt{2}x\right)m$

(c) $(\sqrt{3}-1)xm$

(d) $(\sqrt{3}+1)xm$

Answer 1

Class X

$in△BCD,\tan {45}^0=\frac{h}{y}$

$\to h=y$

$in△ABC,\tan {30}^0=\frac{h}{2x+y}$

$\frac{1}{\sqrt{3}}=\frac{h}{2x+y}$

$2x=\left(\sqrt{3}-1\right)h$ (since h=y )

$h=\frac{2x}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}$

$h=(\sqrt{3}+1)x$