Question

The shadow of tower standing on a level ground is $xm$ long when the Sun's altitude is ${30}^{\circ }$, while it is $ym$ long when the altitude is ${60}^{\circ }$. If the height of the tower is $45\cdot \frac{\sqrt{3}}{2}m$, then $x-y$ is

• A. $45m$
• B. $45\sqrt{3}m$
• C. $\frac{45}{\sqrt{3}}m$
• D. $45\frac{\sqrt{3}}{2}m$

Answer 1

The correct option is A $45m$

In $△CAD,\tan {30}^{\circ }=\frac{45\sqrt{3}/2}{x}$
$\Rightarrow x=\frac{45\sqrt{3}}{2\times \frac{1}{\sqrt{3}}}=\frac{135}{2}m$
And in $△BAD$,
$\tan {60}^{\circ }=\frac{45\sqrt{3}/2}{y}$
$\Rightarrow y=\frac{45}{2}$
$\therefore x-y=\frac{135}{2}-\frac{45}{2}=\frac{90}{2}=45m$.