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)`

Explanation

Let {AB} be the tree, {P} and {Q} be the points from where it is observed.

Draw AC perpendicular to the ground.

Here, B P=a, B Q=b

Let {AC}={h} and {BC}={x}



`Rightarrow {In} triangle {ACP}, tan `

`Rightarrow tan alpha=frac{h}{x+a}`

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