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The shadow of a tower standing on a leve...

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

Text Solution

Verified by Experts

For `trianglePRS, " "cot 60^(@)=(x)/(h)`
For `trianglePQS, " "cot 30^(@) =(d+x)/(h)`
`cot 30^(@) - cot 60^(@)= (d+x-x)/(h)=(d)/(h)`
`h= (d)/(cot 30^(@)-cot 60^(@))=(60)/(sqrt(3)-(1)/(sqrt(3)))`
`=(60sqrt(3))/(3-1)=(60sqrt(3))/(2)`
`30sqrt(3)`
`=51.96m`.
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