A pole 81m high broke at a point but did not separate Its top touched the ground 27 m from - Maths - The Triangle and its Properties

Question

A pole 81m 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?

Shubham Chourasiya · Accepted Answer

suppose the point from which the pole broke is x meters above the ground.Then the length of AC will be (81-x)m.

ΔABC is right angled triangle. By applying Pythagoras theorem ,

${A C}^{2} = {A B}^{2} + {B C}^{2} \Rightarrow {(81 - x)}^{2} = x^{2} + 2 7^{2} \Rightarrow 6561 + x^{2} - 162 x = x^{2} + 729 \Rightarrow 5832 = 162 x \Rightarrow x = 36$

Height from which the pole broke is 36 meters above the ground.

A pole 81m 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?