An important question from RS Aggarwal book of trigonometry in which we have to find the height of the tower and flagpole mounted on the top of tower if there is a vertical tower with a flagpole on the top of the tower. At a point 9 meters away from the foot of the tower the angle of elevation of the top and bottom of the flagpole are 60o and 30o respectively.

Book RS Aggarwal, Class 10,

Topic Height and distance,

Chapter 14, question no 10

In the figure flag pole is AB, BC is tower and CD is base.

In △ACD,

⇒ tan60o=AC/DC

⇒ √3=AC/9

∴ AC=9√3m

In △DBC,

⇒ tan30o=BC/DC

⇒ 1/√3=BC/9

∴ BC=9/√3=3√3m

⇒ AC=AB+BC

⇒ AB=AC−BC

⇒ AB=9√3−3√3=6√3m

∴ Height of the flag pole is 6√3m and that of tower is 3√3m.