A tree breaks due to storm and the broken part bends so that the top of the
tree touches the ground where it makes an angle 30° . The distance between
the foot of the tree to the point where the top touches the ground is 8m. Find
the height of the tree from where it is broken.
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4
Answer:
Let the Height of the Tree =AB+AD
and given that BD=8 m
Now, when it breaks a part of it will remain perpendicular to the ground (AB) and remaining part (AD) will make an angle of 30
o
Now, in △ABD
cos30
o
=
AD
BD
⇒BD=
2
3
AD
⇒AD=
3
2×8
also, in the same Triangle
tan30
o
=
BD
AB
⇒AB=
3
8
∴ Height of tree =AB+AD=(
3
16
+
3
8
)m=
3
24
m=8
3
m
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2
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