Question

Two towers are standing on level ground. From a point on the ground mid-way between them, the angles of elevation of their tops are ${60}^{\circ }$ and ${30}^{\circ }$ respectively. If the height of the first tower is $100m$ the height of the second tower (in $m$) is

• A. $\frac{5}{3}$
• B. $\frac{100}{3}$
• C. $\frac{80}{3}$
• D. $\frac{135}{3}$

Answer 1

The correct option is B $\frac{100}{3}$

Let the height of the second tower be $h.$

In $△ABC,$
$\tan {60}^{\circ }=\frac{AB}{BC}$

$\Rightarrow \sqrt{3}=\frac{100}{x}$

$\Rightarrow x=\frac{100}{\sqrt{3}}$
Now, in $△EDC,$

$\tan {30}^{\circ }=\frac{ED}{DC}$

$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x}$

$\Rightarrow h=\frac{100}{\sqrt{3}}\times \frac{1}{\sqrt{3}}$

$\Rightarrow h=\frac{100}{3}m$