SOLUTION: A telephone pole was bent over at the point 4/9 of the distance from its base to the top. The top of the pole reaches a point on the ground 9 meters from the base of the pole (thus

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A telephone pole was bent over at the point 4/9 of the distance from its base to the top. The top of the pole reaches a point on the ground 9 meters from the base of the pole (thus      Log On


   

Question 684401: A telephone pole was bent over at the point 4/9 of the distance from its base to the top. The top of the pole reaches a point on the ground 9 meters from the base of the pole (thus forming a triangle with the ground). What was the original height of the pole?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the length of pole be x
4x/9 is erect and 5x/9 is the bent portion which is the hypotenuse of the triangle formed.
distance from ground = 9 m
Using Pythagoras theorem
9%5E2%2B%284x%2F9%29%5E2=+%285x%2F9%29%5E2
81%2B16x%5E2%2F81+=+25x%5E2%2F81
25x%5E2%2F81+-16x%5E2%2F81+=+81%0D%0A%0D%0A%7B%7B%7B%2825x%5E2-16x%5E2%29%2F81+=+81
multiply equation by 81
9x%5E2=+81%2A81
/9
x^2= 81*81/9
x^2=81*9
x= +/- 9*3
x= 27 ignore negative value.
Length of pole = 27m