Two poles of equal heights are standing opposite each other on either side of the road,90 m wide . From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$ , respectively. Find the distances of the point from the poles.

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Solution

The above figure represents the situation given in the question
$t a n 30^{\circ} = \frac{A B}{B C} \Rightarrow t a n 30^{\circ} = \frac{A B}{x} \Rightarrow \frac{x}{\sqrt{3}} = A B \dots \dots (1) t a n 60^{\circ} = \frac{E D}{C D} \Rightarrow \sqrt{3} = \frac{E D}{90 - x} \Rightarrow \sqrt{3} (90 - x) = E D \dots \dots (2) B u t E D = A B, t h e r e f o r e f r o m e q (1) a n d (2) \sqrt{3} (90 - x) = \frac{x}{\sqrt{3}} \Rightarrow= 270 - 3 x = x \Rightarrow x = 67.5 m ∴ t h e d i s t a n c e o f t h e p o i n t i s 67.5 m a n d 22.5 m f r o m t h e p o l e s$

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Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$ , respectively. Find the height of the poles and the distances of the point from the poles.

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Two poles of equal heights are standing opposite each other on either side of the road,90 m 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 distances of the point from the poles.

Two poles of equal heights are standing opposite each other on either side of the road,90 m wide . From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$ , respectively. Find the distances of the point from the poles.