Question

a tree standing on a horizontal plane is leaning towards east .  at two points situated at distance a and b exactly due west on it, angle of elevation of top are α and β. prove that height of top from ground is --- (b-a)tanα.tanβ/tanα - tanβ

Answer 1

Heya......

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QUESTION
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a tree standing on a horizontal plane is leaning towards east . at two points situated at distance a and b exactly due west on it, angle of elevation of top are α and β. prove that height of top from ground is --- (b-a)tanα.tanβ/tanα - tanβ
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ANSWER
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Tanα=h/b
So. b= h/tanα

therefore, a=h/tanβ

but, a=b
and when
b-a=h/tanα-h/tanβ
b-a=h(tanβ-tanα/tanα*tanβ)
therefore,
h=b-a(tanα.tanβ/tanα - tanβ)
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Hope It helps

Answer 2

hy
here is your answer
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Let height of the tree = AB = h

Distance between first observe point to foot of tower  BD = a

Distance between secondt 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

Tan α = h / a ⇒ a = h / Tan α ----------(1)

In ΔAcB

Tan β = h / b ⇒ b = h / Tan β ----------(2)

substract (1)  from (2)

 b - a = h / Tan β - h / Tan α

h = (b-a) tanαtanβ / (tanα -tanβ).

∴ height of the top from the ground is = (b-a) tanαtanβ / (tanα -tanβ).
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see in fig