Q45 of 68 Page 9

The distance between two vertical pillars is 100 m, and the height of one is double of the other. The angles of elevation of their tops at a point on the line joining the foot of the two pillars are 60° and 30° respectively. Find their heights.


Let the height of 1st pillar CD = h and height of the 2nd pillar = 2h


It is given that the distance between two vertical pillars is 100m


Now, In right ΔABX, we have





In the right ΔCDE, we have




⇒ 100 – x = √3h






⇒ h = 20√3 m


Hence, the height of the 1st vertical pole, CD = 20√3 m


and the height of the 2nd vertical pole, AB = 2 × 20√3 = 40√3 m


More from this chapter

All 68 →
43

A ladder is placed against a building, and the angle of elevation of the top of the ladder is 60°. The ladder is turned so that it is placed against another building on the other side of the lane and the angle of elevation, in this case, is 45°. If the ladder is 26 m long, then find the width of the lane.

 44

Two pillars of equal height are 64 m apart. The angles of elevation of their tops from any point joining their feet are respectively 30° and 60°. Find the height of the pillars.

 46

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.

 47

The angle of elevation of the top of a tower from the bottom of a tree is 60°, and the angle of elevation of the top of the tree from the foot of the tower is 30°. If the tower is 50 m tall, what is the height of the tree?