an eucalyptus tree breaks due to the storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. the distant from the foot of the tree to the point where top touches the ground is 12.11m find the hieght of the tree
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Answered by
1
Let the broken part of tree be AC
It is given that, distance between foot of the tree B and point C=8m.So, BC=8m
Also, broken parts of tree makes an angle 30
∘
with ground.
So, ∠C=30
∘
We need to find height of the tree
Height of the tree=Height of broken part+Height of remaining tree
=AB+AC
Since, tree was vertical to ground. So, ∠ABC=90
∘
In rightangled △ABC,
cosC=
AC
BC
⇒cos30
∘
=
AC
8
⇒
2
3
=
AC
8
⇒AC=
3
8×2
=
3
16
In rightangled △ABC,
sinC=
AC
AB
⇒sin30
∘
=
3
16
AB
⇒
2
1
=
16
3
×AB
⇒AB=
2
3
16
=
3
8
So, height of the tree=AC+AB=
3
16
+
3
8
=
3
24
3
24
×
3
3
=
3
24
3
=8
3
m
Hence, height of tree is 8
3
m
Answered by
0
Answer:
83 m
Step-by-step explanation:
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