The shadow of a pole standing on a level around is found to be 45 m longer when the Sun's altitude is `30^(@)` than when it was `60^(@)`. Determine the height of the pole. [Given `sqrt(3) = 1.73`]

Explanation

Solution `(x-45)/(h) = cot 30^(@) rArr h = (x+45)/(cot 30^(@))`
`x/h = cot 60^(@)`
Substituting the value of x in the above equation
`h = (h cot 60^(@) + 45)/(cot 30^(@))`
`h cot 30^(@) = h cot 60^(@) + 45`
`h = (45)/(cot 30^(@) - cot 60^(@)) = (45)/(sqrt(3) - (1)/(sqrt(3))) = 38.97` m