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^@`and `30^@`, respectively. Find the height of the poles and the distances of the point from the poles.

Explanation

To solve the problem step by step, we will use trigonometric ratios and the information given in the question.

### Step 1: Understand the Setup
We have two poles of equal height (let's denote the height as \( h \)) standing on either side of a road that is 80 meters wide. From a point \( O \) on the road, the angles of elevation to the tops of the poles are \( 60^\circ \) and \( 30^\circ \).

### Step 2: Define Distances
Let the distance from point \( O \) to the pole with the angle of elevation of \( 60^\circ \) be \( x \) meters. Therefore, the distance from point \( O \) to the other pole will be \( 80 - x \) meters.

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