Question

Two posts are p metres apart and the height of one is double of that of the other. If from the middle-point of the line joining their feet, an observer finds the angular deviations of their tops to be complementary, then the height in metres of the shorter post is

• A. $\frac{p}{\sqrt{2}}$
• B. $\frac{p}{2\sqrt{2}}$
• C. $\sqrt{2}p$
• D. None of these

Answer 1

The correct option is B $\frac{p}{2\sqrt{2}}$


$AB=BC=\frac{p}{2}$
$tan({90}^{\circ }-\theta )=cot\theta =\frac{2h}{\frac{p}{2}}=\frac{4h}{p}$
$tan\theta =\frac{h}{\frac{p}{2}}=\frac{2h}{p}$
$cot\theta \times tan\theta =\frac{4h}{p}\times \frac{2h}{p}=1$
$\therefore h^2=\frac{p^2}{8}$