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A tree breaks due to storm and the broken part bends so that the top of the tree touches making an angle of 30 with it.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.ee.
1258649_65599a33103846a8a90988380673b513.PNG

Solution
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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=BCAC
cos30=8AC
32=8AC
AC=8×23=163
In rightangled ABC,
sinC=ABAC
sin30=AB163
12=316×AB
AB=1623=83
So, height of the tree=AC+AB=163+83=243
243×33=2433=83m
Hence, height of tree is 83m

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A tree breaks due to storm and the broken part bends so that the top of the tree touches making an angle of 30 with it.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.ee.
1258649_65599a33103846a8a90988380673b513.PNG
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