Question

Two poles of equal heights are standing opposite to each other on either side of the road, which is 120 feet wide.From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distance of the point from the poles .​

Answer 1

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Two poles of equal heights are standing opposite to each other on either side of the road, which is 120 feet wide.From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distances of the point from the poles.

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✪ $\huge{\orange{\underline{\red{\mathbb{Solution}}}}}$✪

$From\: the\: figure$

$\: \: \: \tan60° = \frac{h}{x} \: \: \sqrt{3 } = \frac{h}{x} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: h = \sqrt{3} x \: \: ........ \: (1) \\ \\ also \: \tan30° = \frac{h}{120 - x} \: \: \frac{1}{ \sqrt{3} } = \frac{h}{120 - x} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: h = \frac{120 \times x}{ \sqrt{3} } \: \: ....... \: (2) \\ \\ from \: (1) \: and \: (2) \\ \\ ⇒\sqrt{3} x = \frac{120 - x}{ \sqrt{3} } \\ ⇒ \sqrt{3} . \sqrt{3} x = 120 - x \\ ⇒3x = 120 - x \\ ⇒3x + x = 120 \\ ⇒4x = 120 \\ \\ ⇒x = \frac{120}{4} = 30ft. \\ \\ now \: h = \sqrt{3} x = \sqrt{3} \times 30 \\ = 1.732 \times 30 \\ = 51.960 \: feet$

$∴\: distance \:of\:the\:poles=30\:ft.\:and$

$120-30\:fts\:=$$\red{90\:ft.}$

$height\:of\:each\:pole=$$\red{51.96\:ft.}$

Answer 2

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