At a point on a level plane, a tower subtends an angle $α$ and a man h metres high on its topp subtends an angle $β$ . Prove that the height of the tower is $\frac{h tan α}{tan β - tan α}$

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At a point on a level plane, a tower subtends an angle

α

and a man h metres high on its topp subtends an angle

β

. Prove that the height of the tower is

\frac{h tan α}{tan β - tan α}

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Text solutionVerified

I n Δ A BC tan^{2} = \frac{y}{x} x = \frac{y}{t a n ^{2}} I n Δ A D B tan β = \frac{n + y}{x} tan β = \frac{n + y}{y / t a n ^{2}} = \frac{( n + y ) t a n x}{y} y tan β = tan x \cdot h + tan 2 \cdot y y (tan β - tan^{2}) = h tan α y = \frac{h + t a n α}{t a n β - t a n α}

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Question Text	At a point on a level plane, a tower subtends an angle $α$ and a man h metres high on its topp subtends an angle $β$ . Prove that the height of the tower is $\frac{h tan α}{tan β - tan α}$
Answer Type	Text solution:1
Upvotes	150