A palm tree 90ft high is broken by wind and its upper part meets the ground at an angle of 30 degree .Find the distance of the point where the top of the tree meets the ground, from its root . Find also the height at which the tree was broken.(Take √3=1.732)
Please solve it fast.
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Answer:
Segment AB represents the height of the tree.
The tree breaks at point D.
∴ Segment AD is the broken part of tree which then takes the position of DC.
∴AD=DC
Given m∠DCB=30
∘
,BC=30m
In right angled ΔDBC,
tan30
∘
=
BC
BD
⇒
3
1
=
30
BD
⇒BD=
3
30
∴BD=10
3
m
Also cos30
∘
=
DC
BC
⇒
2
3
=
DC
30
⇒DC=
3
60
∴DC=20
3
m
Hence AD=DC=20
3
m
From the figure, AB=AD+DB
∴AB=20
3
+10
3
⇒AB=30
3
m
∴AB=30×1.73
∴AB=51.9m
Hence, the height of tree is 51.9m.
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