The two palm tree are equal height are standing opposite each other on either side of the river which is 80 metre wide from a point between them on river the angle of elevation of the top of the trees are 60 degree and 30 degree respectively find the height of the trees and the distance of the point O from the tree
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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
solution
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