Question

11. A TV tower stands vertically on a bank
of a canal. From a point on the other
bank directly opposite the tower, the
angle of elevation of the top of the
tower is 60°. From another point 20 m
away from this point on the line joing
this point to the foot of the tower, the
angle of elevation of the top of the
tower is 30° (see Fig. 9.12). Find the
height of the tower and the width of
the canal.​

Answer 1

In ∆ABC,

AB/BC= tan60°

h/x = Root 3

h= Root 3x •••••••1.

In ∆ABD,

AB/BD= tan30°

AB/ 20+x= 1/Root 3

AB = 20+x/ Root 3••••••••2.

From 1. and 2.

Root 3x= 20+x/ Root 3

Now, Root 3x × Root 3x+x= 20

3x-x=20

2x=20

x=10

Now, From 1.

h= Root 3(10)

= 1.732×10

= 17.32m

Hence, Proved