A TV tower stands vertically on a
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.
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From the top of a 7 m high building, the angle of el
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Answer:
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Answer:
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.
cot60
o
=x/h
1/
3
=x/h
x=h/
3
....(1)
From right △BAD:
cot30
o
=AD/AB
3
=(x+20)/h
x=h
3
−20....(2)
h=10
3
From (1): x=(10
3
)/
3
=10
Therefore, the width of the canal is 10 m and height of the canal is 10
3
m.
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