Question 14 Only Please tell fast
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Question :--------- we have to prove Cot θ = (b Cot α - aCot β) / (b - a).
Let height of the tower DE = h
Distance between first station to foot of tower AD = a + x
Distance between second station to foot of tower BD = b +x
Distance between C and D = x
Give α, β are the angle of elevation two stations to top of the tower
that is ∠DAE = α, ∠DBE = β ,∠DCE =θ .
In Δ ADE
Cot θ = x / h ----------------→(1)
In Δ BDE
Cot β = (b+x) / h
(b+x) = h Cot β (multiply a on both sides )
(ab+ax) = ha Cot β ----------------→(2)
In Δ CDE
Cot α = (a+x) / h
(a+x) = h Cot α (multiply b on both sides )
(ab+bx) = hb Cot α ----------------→(3)
substract (3) - (2)
(b - a)x = h (b Cot α - aCot β)
x / h = (b Cot α - aCot β) / (b - a)
Cot θ=(bCotα-aCotβ)/(b - a)
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