Q. 363.6( 11 Votes )

A 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 distance from the foot of the tree to the point where the top touches the ground is 10 metres. Find the height of the tree.

Answer :

In fig.BD is the height of the tree. Let the broken part touches the ground at point C


BD = AB+AD


in ∆ABC


tan 30° =


=


√3h = 10


h =


h = m. -------(1)


Again ∆ABC.


COS 30° =



√3


=


= ------(2)



Therefore height of tree = () m.


Adding eqn. (1) and (2) we get,


+


= 10√3


10× 1.732 17.32 m.


Therefore height of tree is 17.32 m.


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