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Let the height of the tree AB=h
Distance between first observe point to foot of tower BD = a
Distance between second observe point to foot of tower BC = b
α, β are the angle of elevation to the top of the tower.
∠ACB = α and ∠ADB = β.
In ΔADB,
tanα=h/a
a=h/tanα---(1)
In △ACB,
tanβ=h/b
b=h/tanβ---(2)
Subtract (1) from (2)
b-a=h/tanβ -h/tanα
=>(b-a) tanα tan β/ tanα- tan β
Hence proved.
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