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A tree standing on horizontal plane is l...

A tree standing on horizontal plane is leaning towards east. At two points situated at distances a and b exactly due west on it, angles of elevation of the top are respectively `alpha` and `beta`. Prove that height of the top from the ground is `((b-a).tanalpha.tanbeta)/(tanalpha-tanbeta)`

Text Solution

Verified by Experts

We can draw a diagram with the given details.
Please refer to video for the diagram.
Here, height of top from the ground ` = OB = h`
`AC = a, AD = b, OB =x`
`/_OCB = alpha, /_ODB = beta`
`:.tan alpha = (OB)/(OC) `
`=> tan alpha = h/(x+a)`
`h = tan alpha(x+a)->(1)`
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