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A wireless pole 25 metres high is fixed on the top of a verand

Question

A wireless pole 25 metres high is fixed on the top of a verandah of a house which is 15 metres high. At a point R on the ground directly opposite the wireless pole and verandah subtend equal angles. Find the distance of R from the verandah.

30

15

25

40

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A wireless pole 25 metres high is fixed on the top of a verandah of a house which is 15 metres high. At a point R on the ground directly opposite the wireless pole and verandah subtend equal angles. Find the distance of R from the verandah.

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Text solutionVerified

Let the distance of

R

from verandah be

x

Given height of the pole

= 25 m

height of the house

= 15 m

△ PQR, tan θ = \frac{15}{x}

△ MPR, tan 2 θ = \frac{40}{x}

⟹ \frac{2 tan θ}{1 - tan ^{2} θ} = \frac{40}{x}

⟹ \frac{2 \times \frac{15}{x}}{1 - ( \frac{15}{x} ) ^{2}} = \frac{40}{x}

⟹ \frac{3 x}{x ^{2} - 225} = \frac{4}{x}

⟹ x^{2} = 4 \times 225

⟹ x = 30 m

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Question Text	A wireless pole 25 metres high is fixed on the top of a verandah of a house which is 15 metres high. At a point R on the ground directly opposite the wireless pole and verandah subtend equal angles. Find the distance of R from the verandah.
Answer Type	Text solution:1
Upvotes	150

A wireless pole 25 metres high is fixed on the top of a verandah of a house which is 15 metres high. At a point R on the ground directly opposite the wireless pole and verandah subtend equal angles. Find the distance of R from the verandah.

Text solutionVerified

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