Question

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angels of elevation of the top of the poles are 60° and 30° respectively.

Find the height of the poles and the distances of the point from the poles.

Answer 1

Let AC and BD be the two poles of the same height h m.

Given AB = 80 m

Let, AP = x m, therefore, PB = (80 − x) m

In triangles APC and BPD

`tan 30^@((AC)/(AP))=h/x` and `tan60^@((BD)/(AB))=H/(80-x)`

`therefore(tan30^@)/(tan60^@)=x/(h/(80-x))=(80-x)/x`

`rArr1/3=(80-x)/xrArr=60m`

`thereforeh=xtan30^@` `60/sqrt3=20sqrt3m.`

Therefore, the height of the poles is `20sqrt3`and the distances of the point from the poles are 60 m and 20 m.