Question

Question 14 Only Please tell fast

Answer 1

Question :--------- we have to prove Cot θ = (b Cot α - aCot β) / (b - a).

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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)