Two poles of height 18 m each are standing opposite each other on either side of the road. 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 width of the road.

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Solution

The above figure represents the situation given in the question. Let BC=x and CD=y
$t a n 30^{\circ} = \frac{A B}{B C} \Rightarrow t a n 30^{\circ} = \frac{A B}{x} \Rightarrow \frac{x}{\sqrt{3}} = A B \dots \dots (1) t a n 60^{\circ} = \frac{E D}{C D} \Rightarrow \sqrt{3} = \frac{E D}{y} \Rightarrow \sqrt{3} (y) = E D \dots \dots (2) B u t E D = A B, t h e r e f o r e f r o m e q (1) a n d (2) B D = B C + C D \Rightarrow B C = 24 m \sqrt{3} ∴ t h e r o a d i s 24 m \sqrt{3}$

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Q. Two poles of equal heights are standing opposite each other on either side of the road which is

80

m wide. From the points between them on the road, the elevation of the top of the poles are

60^{\circ}

and

30^{\circ}

respectively. Find the height of the poles.

Question 10
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 height 18 m each are standing opposite each other on either side of the road. 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 width of the road.

The above figure represents the situation given in the question. Let BC=x and CD=y tan30∘=ABBC⇒tan30∘=ABx⇒x√3=AB……(1)tan60∘=EDCD⇒√3=EDy⇒√3(y)=ED……(2)But ED=AB, therefore from eq(1) and (2) BD=BC+CD⇒BC=24m√3∴ the road is 24m√3

Two poles of height 18 m each are standing opposite each other on either side of the road. 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 width of the road.