Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower. [Use √3 = 1.732]

Answer 1

Draw a figure based on given instructions:

From figure:

AB = height of the tower, say h meters

In right triangle BOA,

cot 30° = OA/AB

√3 = OA/h

or OA = h√3 …(1)

From another right triangle COA,

cot 60° = OA/AC

1/√3 = OA/(h+6)

or OA = (h+6)/√3 …(2)

form (1) and (2)

(h+6)/√3 = h√3

h = 3

Therefore the height of the tower is 3 meters.