Question

Two stations due south of a leaning tower which leans towards the north are at distance a and b from its foot . If alpha and beta are the angle of elevation of top of the tower from these stations, then prove that its angle of inclination theata to the horizontal is given by cot theata = bcot alpha -acot beta/ b-a

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Raghunath answered 3 year(s) ago

Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot if α and β beelevationopoffrom thesestati, Prove that its inclination θ to be

Horizontal is given by 

              Cot θ =              b cot α - α cot β/b-a

Class-X Maths

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Asked by Rohit

Mar 1

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Raghunath , SubjectMatterExpert

Member since Apr 11 2014

Sol :

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 = (b Cot α - aCot β) / (b - a).