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At a distance a from the foot of a tower AB of known height b

Question

At a distance a from the foot of a tower $A B$ of known height $b$ a flagstaff $BC$ and the tower subtend equal angles, height of the flagstaff is

\frac{a ^{2} + b ^{2}}{a ^{2} - b ^{2}}

\frac{a ^{2} - b ^{2}}{a ^{2} + b ^{2}}

\frac{a ( a ^{2} - b ^{2} )}{a ^{2} + b ^{2}}

\frac{b ( a ^{2} + b ^{2} )}{( a ^{2} - b ^{2} )}

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At a distance a from the foot of a tower

A B

of known height

b

a flagstaff

BC

and the tower subtend equal angles, height of the flagstaff is

14 mins ago

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14 mins ago

Text solutionVerified

Given

∠ A PB = ∠ BP A = θ (s a y)

Δ A BP, ∠ B A P = 90° tan θ = \frac{b}{a}

Δ C A P, ∠ C A P = 90° tan (2 θ) = \frac{C D + b}{a} tan θ = \frac{2 tan θ}{1 - tan ^{2} θ} = \frac{\frac{2 b}{a}}{1 - \frac{b ^{2}}{a ^{2}}} = \frac{2 ab}{a ^{2} - b ^{2}} (∵ tan θ = \frac{b}{a}) ∴ \frac{2 ab}{a ^{2} - b ^{2}} = \frac{CB + b}{a} \Rightarrow \frac{2 a ^{2} b}{a ^{2} - b ^{2}} = CB + b \Rightarrow CB = \frac{2 a ^{2} b}{a ^{2} - b ^{2}} - b = \frac{2 a ^{2} b - a ^{2} b + b ^{3}}{a ^{2} - b ^{2}} = \frac{a ^{2} b + b ^{3}}{a ^{2} - b ^{2}} \Rightarrow CB = \frac{b ( a ^{2} + b ^{2} )}{( a ^{2} - b ^{2} )}

Answer D

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Question Text	At a distance a from the foot of a tower $A B$ of known height $b$ a flagstaff $BC$ and the tower subtend equal angles, height of the flagstaff is
Answer Type	Text solution:1
Upvotes	150