(Q3) A TV tower stands vertically on the side of a road. From a point on the other side directly opposite to the tower, the angle of elevation of the top of tower is 60^o. From another point 10 m away from this point, on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30^o. Find the height of the tower and the width of the road.

Answer :

Let the height of the tower = h mts say

Width of the road be = x m.

Distance between two points of observation = 10 cm.

Angles of elevation from the two points = 60^o and 30^o.

h = √ x .....(1)

From equations (1) and (2) h

√ × √ x = + x

x - x =

x =

x = m

∴ Width of the road = m

Now Height of the tower = √ x = √ m.