SOLUTION: A 15 feet ladder is 5 feet away from a wall. How far above the floor is the top of the ladder?

Algebra ->  Pythagorean-theorem -> SOLUTION: A 15 feet ladder is 5 feet away from a wall. How far above the floor is the top of the ladder?      Log On


   

Question 121931: A 15 feet ladder is 5 feet away from a wall. How far above the floor is the top of the ladder?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:


Since we can see that the triangle has legs of x and 5 with a hypotenuse of 15, we can use Pythagoreans theorem to find the unknown side.


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%2B5%5E2=15%5E2 Plug in a=x, b=5, and c=15. Now lets solve for x


+x++%5E+2+%2B+2+5+=+2+2+5 Square each individual term



+x++%5E+2+=+2+2+5+-+2+5 Subtract 25 from both sides


+x++%5E+2+=+2+0+0 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+2+0+0+%29 Take the square root of both sides



x=10%2Asqrt%282%29 Simplify the square root

Which approximates to...
x+=+1+4+.+1+4+2+1+3+5+6+2+3+7+3+1

So our answer is
x+=+1+4+.+1+4+2+1+3+5+6+2+3+7+3+1



So the top of the ladder is about 14.14 feet about the floor