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The angle of elevation of the top of a ...

The angle of elevation of the top of a tower from a point on the ground is `30^(@)`. After walking `40sqrt3` m towards the tower, the angle of elevation becomes `60^(@)`. Find the height of the tower.

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Let AB be a tower of height 'h' metres. From points D and C on the ground, the angle of elevation of top A of the tower are `30^(@)" and "60^(@)` respectively.
Given that `CD=40sqrt3 m`
In `DeltaABC`
`tan60^(@)=(AB)/(BC)rArrsqrt3=h/x`
`rArr x=h/sqrt3 ...(i)`
In `DeltaABD`
`tan30^(@)=(AB)/(BD)rArr1/sqrt3=h/(40sqrt3+x)`
`rArrsqrt3h=40sqrt3+xrArrsqrt3h=40sqrt3+h/sqrt3`
`rArr 3h=120+h" "2h=120`
`rArr h=60`
`:." Height of the tower "=60 m`
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