Question

The angle of elevation of the top of a tower as observed from a point on the horizontal ground is $x$. If we move a distance $d$ towards the flux of the tower, the angle of elevation increases to $y$, then the height of the tower is

• A. $\frac{d\tan x\tan y}{\tan y-\tan x}$
• B. $d(\tan y+\tan x)$
• C. $d(\tan y-\tan x)$
• D. $\frac{d\tan x\tan y}{\tan y+\tan x}$

Answer 1

Answer: (A)

$\frac{d\tan x\tan y}{\tan y-\tan x}$

In $△ABC,$

$\Rightarrow \tan y=\frac{h}{z}$

$\Rightarrow h=z\tan y...\left(1\right)$

In $△ADC,$

$\tan x=\frac{h}{d+z}$
$\Rightarrow \tan x=\frac{z\tan y}{d+z}$ [from (1)]

$\Rightarrow z\left(\tan y-\tan x\right)=d\tan x$

$\therefore h=\frac{d\tan x\tan y}{\tan y-\tan x}$