Q. 24.4( 292 Votes )
A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree
Let BAC be the tree.
Now, due to storm AC is broken and leans to make a shape as right-angled triangle shown in figure.
AC is the broken part of the tree and AB is the part which is still upright.
Distance from tree foot to where top touches, BC = 8 m
∠ BCA = 30o
Clearly, Sum of AB and AC will give the height of the tree.
In Δ ABC:
Height of tree= AB + AC
=rationalizing, we get
= 8√3 m
Hence, height of the tree is 8√3 m
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