Question

The angle of elevation of the top of a tower ad observed from a point on the horizontal ground is $x$. If we move a distance ${}^{\prime }{d}^{\prime }$ towards the foot of the tower, the angle of elevation increases to $y$, then the height if 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

The correct option is A $\frac{d\tan x\tan y}{\tan y-\tan x}$

Let height of the tower , $AB=h$

From $△ADB,\tan y=\frac{h}{BD}$

or $BD=h\cot y$ ....$\left(i\right)$

From $△ADB$ and $△ACB$

$\tan x=\frac{h}{d+DB}$ or $d+DB=h\cot x$

Or

$h(\cot x-\cot y)=d$

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

$=\frac{d}{\frac{1}{\tan x}-\frac{1}{\tan y}}=\frac{d\tan x.\tan y}{\tan y-\tan x}$