Two poles of equal heights are standing opposite each other on either sideof the roads, which is 80 m wide. From a point between them on theroad, the angles of elevation of the top of the poles are 60o and 30orespectively. Find the height of the poles and the distances of the pointfrom the poles.

Solution

$Let AC and BD be the two poles of the same height h m . Given : AB = 80 m Let AP = x m, therefore, PB = (80 - x) m In ∆ APC, \tan 30 ° = \frac{AC}{AP} \frac{1}{\sqrt{3}} = \frac{h}{x} . . . . . . . . . (1) In ∆ BPD, \tan 60 ° = \frac{BD}{AB} \sqrt{3} = \frac{h}{80 - x} . . . . . . . . . . . . . (2) Dividing (1) by (2), \frac{\frac{1}{\sqrt{3}}}{\sqrt{3}} = \frac{\frac{h}{x}}{\frac{h}{80 - x}} \Rightarrow \frac{1}{3} = \frac{80 - x}{x} \Rightarrow x = 240 - 3 x \Rightarrow 4 x = 240 \Rightarrow x = 60 From (1), \frac{1}{\sqrt{3}} = \frac{h}{x} \Rightarrow h = \frac{60}{\sqrt{3}} = 20 \sqrt{3} m Thus, the height of both the poles is 20 \sqrt{3} m and the distance of the point from the poles are 60 m and 20 m .$

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Some Applications Of Trigonometry

Two poles of equal heights are standing opposite each other on either sideof the roads, which is 80 m wide. From a point between them on theroad, the angles of elevation of the top of the poles are 60o and 30orespectively. Find the height of the poles and the distances of the pointfrom the poles.

Some More Questions From Some Applications of Trigonometry Chapter

Choose the correct option and justify your choice:
sin 2A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Some Applications Of Trigonometry

Two poles of equal heights are standing opposite each other on either sideof the roads, which is 80 m wide. From a point between them on theroad, the angles of elevation of the top of the poles are 60o and 30orespectively. Find the height of the poles and the distances of the pointfrom the poles.

Some More Questions From Some Applications of Trigonometry Chapter

Choose the correct option and justify your choice:sin 2A = 2 sin A is true when A = (A) 0° (B) 30° (C) 45° (D) 60°

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Choose the correct option and justify your choice:
sin 2A = 2 sin A is true when A =
(A) 0° (B) 30° (C) 45° (D) 60°