The top of a pole is 12 m from the ground. If the pole is tilted towards a point on the ground the top is 8 m from the point and..6 m from the ground.  How far from the bottom of the pole is the...

The top of a pole is 12 m from the ground. If the pole is tilted towards a point on the ground the top is 8 m from the point and..

6 m from the ground.  How far from the bottom of the pole is the point.

justaguide | College Teacher | (Level 2) Distinguished Educator

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The top of a pole is 12 m from the ground. The pole is tilted towards a point on the ground, after doing which the top is 8 m from the point and 6 m from the ground.

Let the top of the pole be a point T and the bottom a point B. Drop a vertical line from the point T to the ground and the point where it touches the ground be C. As the top of the pole is 6 m from the ground after it is tilted, TC is 6. If the point towards which the pole is being bent is X, two right triangles are created.

One is TBC which has sides 12, 6 and BC. The other TXC has sides 8, 6 and XC. The distance to be determined is BX.

BC = `sqrt(12^2 - 6^2)` and CX = `sqrt(8^2 - 6^2)`

=> BC = `sqrt 108` and CX = `sqrt 28`

BX = `sqrt 108 + sqrt 28`

=> `2*sqrt 27 + 2*sqrt 7`

`~~` 15.68 m

The point towards which the pole is bent is approximately 15.68 m form the bottom of the pole.