Question

On one side of a road of width $d$ metres there is a point of observation $P$ at a height $h$ metres from the ground. If a tree on the other side of the road, makes a right angle at $P$, height of the tree in metres is:

• A. $\frac{h^2-d^2}{h}$
• B. $\frac{h^2+d^2}{h}$
• C. $\frac{d^2-h^2}{h}$
• D. $\frac{2d^2+h^2}{h}$

Answer 1

The correct option is B $\frac{h^2+d^2}{h}$

In $△PBA,{AP}^2=h^2+d^2$

In $△PCD,{PC}^2={(H-h)}^2+d^2$

In $△ADC,{AC}^2={AP}^2+{PC}^2$

$H^2=h^2+d^2+{(H-h)}^2+d^2$

$H^2=h^2+2d^2+H^2+h^2-2Hh$

$2Hh=2h^2+2d^2\Rightarrow H=\frac{h^2+d^2}{h}$