Question

Two posts are k meters apart. if from the middle point of the line joining their feet, an observer finds the angles of elevations of their tops to be ${60}^{\circ }$ and ${30}^{\circ }$ respectively, then the ratio of height of the posts respectively is

• A. $\sqrt{3}$
• B. $\frac{5}{\sqrt{3}}$
• C. $k\sqrt{3}$
• D. 3

Answer 1

The correct option is D 3

Let the two posts be $AB$ and $ED$ of heights $h_{1}and{h}_2$ respectively.
Let the angle of elevation for the top of $AB$ be ${60}^{\circ }$ and the top of $ED$ be ${30}^{\circ }$ respectively.

Given, $BC=CD=\frac{k}{2}$
In $\Delta ABC$,
$\frac{h_1}{k/2}=\tan {60}^{\circ }\Rightarrow h_1=\frac{k}{2}\times \sqrt{3}=\frac{k\sqrt{3}}{2}$
$In\Delta EDC$,
$\frac{h_2}{k/2}=\tan {30}^{\circ }\Rightarrow h_2=\frac{k}{2}\times \frac{1}{\sqrt{3}}=\frac{k}{2\sqrt{3}}$
$\therefore \frac{h_1}{h_2}=\frac{\frac{k\sqrt{3}}{2}}{\frac{k}{2\sqrt{3}}}=\sqrt{3}\times \sqrt{3}=3$