Question

Two posts are x meters apart and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then the height (in meters) of the shorter post is,

• A.
• B.
• C.
• D.

Answer 1

The correct option is C


Above figure is the representation of the given question
We have to find h in terms of x
$tan\theta =\frac{h}{\left(\frac{x}{2}\right)}=\frac{2h}{x}....\left(i\right)$
$tan({90}^{\circ }-\theta )=cot\theta =\frac{2h}{\left(\frac{x}{2}\right)}=\frac{4h}{x}....\left(ii\right)$
Multiplying (i) and (ii),
$tan\theta \times cot\theta =\left(\frac{2h}{x}\right)\times \left(\frac{4h}{x}\right)$
$\Rightarrow 1=\frac{8h^2}{x^2}$
$\Rightarrow h=\frac{x}{2\sqrt{2}}$