SOLUTION: hello again guys...!Here's my question: A vertical pole was broken by the wind. The upper part, still attached, reached a point on the level ground 15 feet from the base. If the

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: hello again guys...!Here's my question: A vertical pole was broken by the wind. The upper part, still attached, reached a point on the level ground 15 feet from the base. If the      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 146493: hello again guys...!Here's my question:
A vertical pole was broken by the wind. The upper part, still attached, reached a point on the level ground 15 feet from the base. If the upper part is 9 feet longer than the lower part, how tall was the pole?
Found 2 solutions by jim_thompson5910, checkley77:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length of the lower part

If you draw the triangle, you'll get




So we can use Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse


x%5E2%2B15%5E2=%28x%2B9%29%5E2 Plug in a=x, b=15 and c=x%2B9


x%5E2%2B225=%28x%2B9%29%5E2 Square 15 to get 225


x%5E2%2B225=x%5E2%2B18x%2B81 FOIL


x%5E2%2B225-x%5E2-18x-81=0 Get all terms to the left side.


-18x%2B144=0 Combine like terms.



-18x=0-144 Subtract 144 from both sides.


-18x=-144 Combine like terms on the right side.


x=%28-144%29%2F%28-18%29 Divide both sides by -18 to isolate x.


x=8 Reduce.

So the length of the lower part is 8 feet. Now let's find the length of the upper part:


x%2B9 Start with the expression for length of the upper part


8%2B9 Plug in x=8


17


So the length of the upper part is 17 feet


This means that the total length is 8%2B17=25 feet

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
15^2+X^2=(X+9)^2
225+X^2=X^2+18X+81
18X=225-81
18X=144
X=144/18
X=8 FEET FOR THE LOWER PART OF THE POLE.
8+9=17 FEET FOR THE UPPER PART OF THE POLE.
PROOF:
15^2+8^2=17^2
225+64=289
289=289