Two palm trees are of equal heights and are standing opposite to each other on either side of the river which is 80m wide. From a point ‘O’ between them on the rivers the angles of elevation of the top of the trees are 600 & 300 respectively. Find the height of the trees and the distance of the point ‘O’ from the trees.
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Answer:
Consider the above figure
tan60
0
=
80−x
b
⇒
3
=
80−x
b
⇒b=
3
x−80
3
....(i)
and,
tan30
0
=
3
1
=
x
a
x=a
3
...(ii)
b=3a−80
3
Or
3a−b=80
3
Now it is given that the heights are equal.
Hence
a=b=h
Therefore
2h=80
3
h=20
3
=2(17.32)
=34.64m
Hence
x=h
3
=20(3)=60m
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