Question

Two vertical poles $20m$ and $80m$ high stand apart $50m$ on a horizontal plane. The height of the point of intersection of the lines joining the top of each pole to the foot of the other is

• A. $15m$
• B. $16m$
• C. $18m$
• D. $50m$

Answer 1

The correct option is B $16m$

From figure ,The projection of the intersection point divides the base line in the ration $1:4$ So $BD=10$ and $DE=40$

In $\Delta ABE$

$\tan E=\frac{2}{5}\cdots \left(1\right)$

In $\Delta CDE$

$\tan E=\frac{CD}{40}\cdots \left(2\right)$

From $\left(1\right)\left(2\right)$

$⟹CD=16$