Question

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. 12.12). Find the
height of the tower and the width of
the canal.​

Answer 1

Step-by-step explanation:

Answer

In the figure, let AB be the tower and AC be the canal. C is the point on the other side of the canal directly opposite the tower.

Let AB=h,CA=x and CD=20

From right △BAC.

cot60o=x/h

1/3=x/h

x=h/3....(1)

From right △BAD:

cot30o=AD/AB

3=(x+20)/h

x=h3−20....(2)

h=103

From (1): x=(103)/3=10

Therefore, the width of the canal is 10 m and height of the canal is 103 m.

hope it helps