Question

$ABC$ is an equilateral triangular plot. An electric pole stands at the vertex and makes an angle of $60°$ at either of the other two vertices. If the height of the triangle is $100m$, then the height of the pole is

• A. $100$ m
• B. $150$ m
• C. $200$ m
• D. $300$ m

Answer 1

The correct option is C

$200$ m

Explanation for the correct option:

Step-1: Draw the figure according to the situation:

Let $AP$ be the electric pole of height h.

$\therefore$$\frac{AB}{h}=cot60°$

$\begin{array}{rcl}& \Rightarrow & AB=\frac{h}{\surd 3}\\ & =& AC\\ & =& BC\end{array}$

$\because AD=100m$

Step-2: Height and side relation of equilateral traingle:

As we know, $B{D}^2=A{B}^2–A{D}^2$

$\Rightarrow$${\left(\frac{1}{2}\times \frac{h}{\sqrt{3}}\right)}^2={\left(\frac{h}{\sqrt{3}}\right)}^2–{100}^2$

$\Rightarrow$ $\frac{h^2}{12}=\frac{h^2}{3}-{100}^2$

$\Rightarrow$ $\frac{h^2}{3}-\frac{h^2}{12}={100}^2$

$\Rightarrow$ $\frac{3h^2}{12}={100}^2$

$\Rightarrow$ $\frac{h^2}{4}={100}^2$

$\Rightarrow$ $h^2=4\times {100}^2$

$\Rightarrow$ $h=200m$

Hence, option ‘C’ is correct.