Q46 of 68 Page 9

Two pillars of equal height stand on either side of roadway which is 30 m wide. At a point in the roadway between the pillars, the elevations of the tops of the pillars are 60° and 30°. Find the heights of the pillars and the position of the point.


Let the height of the equal pillars AB = CD = h


Given the width of the road, BD = 30m


Let BE = x. Hence, DE = 30 – x


Now, In right ΔABE, we have





In the right ΔCDE, we have




⇒ 30 – x = √3h








⇒ h = 12.99m


Hence, the height of the equal pillars AB = CD = 12.99 m


The distance of a point from one pillar is



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