SOLUTION: Due to a storm, a flagpole broke at a certain point. The top part tipped over like a hinge, with the tip hitting the ground at a point 20 feet from the flagpole's base. The flag

Algebra ->  Trigonometry-basics -> SOLUTION: Due to a storm, a flagpole broke at a certain point. The top part tipped over like a hinge, with the tip hitting the ground at a point 20 feet from the flagpole's base. The flag      Log On


   

Question 715244: Due to a storm, a flagpole broke at a certain point. The top part tipped over like a hinge, with the tip hitting the ground at a point 20 feet from the flagpole's base.
The flagpole was rewelded, but another storm broke it again at a point 5 feet lower than the previous break. And, this time the tip hit the ground at a point 30 feet from the base.
How tall was the flagpole?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let the broken part length be y
let the remaining lenngth be x
distance from base of pole = 20ft
they form a right triangle
y%5E2=x%5E2%2B%2820%29%5E2 by Pythagoras theorem
y%5E2-x%5E2=400
Second condition
it breaks 5feet below
The broken part length = y+5
The remaining part length =- x-5
distance from base of pole = 30 ft
%28y%2B5%29%5E2=+%28x-5%29%5E2%2B%2830%29%5E2
y%5E2%2B10y%2B25+=+x%5E2-10x%2B25%2B900
y%5E2-x%5E2=+-10x-10y%2B900
400=+-10x-10y%2B900
10x+10y=500
/10
x+y= 50
But x+y is the length of the flag pole