Question

Two points '$A$' and '$B$' are in a straight line at a distance of $100$ metre and $25$ metre from base of a minarate respectively. Angle of elevation of the building at the points $A$ and $B$ is complementary. Find the height of the building.

Answer 1

Let $O$ be the base of building and $P$ be the top of the building.

Let height of the building $=OP=h$

According to the given condition,

$OB=25cm$ and $OA=100cm$

$\angle PBO=\angle B$ and $\angle PAO=\angle A$

$\because$ $\angle B$ and $\angle A$ are complimentary,

$\Rightarrow \angle B=\angle ({90}^o-\angle A)$

$\Rightarrow tan\angle B=tan\angle ({90}^o-\angle A)$

$\Rightarrow \tan B=\cot A$

$\tan B=\frac{h}{25}$

$\cot A=\frac{100}{h}$

$\Rightarrow \frac{h}{25}=\frac{100}{h}\Rightarrow h^2=2500$

$\Rightarrow h=50m$