Question

Two vertical poles 20 m and 80 m high stand apart 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' meters. Find 'a'.

Answer 1

Let the height be x.

The horizontal distance from the intersection point to the 20m pole a.

The horizontal distance from the intersection point to the 80m pole b.

$\frac{a+b}{20}=\frac{b}{x}$

$=\frac{40(a+b)}{80}$

$\frac{a+b}{80}=\frac{a}{x}$

adding both sides

$\frac{50(a+b)}{80}=\frac{a+b}{x}$

$x=\frac{80}{50}$

$x=1.6m$