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A vertical tower Stands on a horizontal ...

A vertical tower Stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of Elevation of the bottom and the top of the flag staff are `alpha and beta` respectively Prove that the height of the tower is `(htanalpha)/(tanbeta - tanalpha)`

Text Solution

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We can draw a diagram with the given details.
Please refer to video for the diagram.
Here, height of the tower ` = BC = x`
`AB = h, CD = y`
`/_CDB = alpha, /_CDA = beta`
`:.tan alpha = (BC)/(CD) `
`=> tan alpha = x/y`
`y = x/ tan alpha->(1)`
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