The shadow of a tower standing on a level plane is found to be 50 m longer when the Sun's elevation is `30^(@)` than when it is `60^(@).` The height of the tower is

Explanation

In fig. 1(c ). 14.

`cot 30^@ = (OB)/(h) and cot 60^@ = (AB)/(h)`
`cot 30^@ - cot 60^@ = (OB - AB)/(h) = (OA)/(h) = (50)/(h)`
`sqrt3 - (1)/(sqrt3) =(50)/(h) = (2)/(sqrt3)`
`h = (50sqrt3)/(2) = 43.3m`