The two palm trees are of equal heights and are standing opposite each
other on either side of the river, which is 80 m wide. From a point O
between them on the river the angles of elevation of the top of the trees
are 60° and 30°, respectively. Find the height of the trees and the
distances of the point O from the trees.
Answers
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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
Step-by-step explanation:
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