Question

Example 13. Two stations due south of a leaning tower which leads towards the north are at
distances a and ) from its foot. I o, be the elevations of the top of the tower from these stations,
b cot a-a cot B
prove that its inclination to the horizontal is given by cot e =
b-a​

Answer 1

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Some Applications of Trigonometry

Heights and Distances

Two stations due South of a...

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Asked on November 22, 2019 by

Yuraj Tehreem

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 are the elevations of the top of the tower from these stations, then prove that its inclination θ to the horizontal is given by

cotθ=

b−a

bcotα−acotβ

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ANSWER

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 CandD=x

Give α, β are the angle of elevation two stations to top of the tower

thatis∠DAE=α,∠DBE=β,∠DCE=θ

InΔADE

Cotθ=x/h−−−−−−−−−−−−−−−−→(1)

InΔBDE

Cotβ=(b+x)/h

(b+x)=hCotβ (multiply a on both sides )

(ab+ax)=haCotβ−−−−−−−−−−−−−−−−→(2)

InΔCDE

Cotα=(a+x)/h

(a+x)=hCotα (multiply b on both sides )

(ab+bx)=hbCotα−−−−−−−−−−−−−−−−→(3)

substract(3)−(2)

(b−a)x=h(bCotα−aCotβ)

x/h=(bCotα−aCotβ)/(b−a)

Cotθ=(bCotα−aCotβ)/(b−a).

Answer 2

Answer:

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