Question:
a pole 81 m high broke at a point but did not separate. its top touched the ground 27 m from its base. at what height above the ground did the pole break
Answer:
Let at point C, the pole break down and touches the ground.
Let BC = x, So AB = BC = 81-x
Given base is 21m. So CD = 21
Now from Pythagoras Theorem
BD2 = CD2 + BC2
=> (81-x)2 = 212 + x2
=> 6561 + x2 - 162x = 729 + x2
=> 6561 - 729 = 162x
=> 5832 = 162x
=> x = 5832/162
=> x =36
So the pole break down at height 36 m from the ground.
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