SOLUTION: I need help with this problem please. The answer is suppose to be to the nearest thousandth. The base of an 18-ft ladder is 4 ft away from a wall. How far above the floor is the

Algebra ->  Pythagorean-theorem -> SOLUTION: I need help with this problem please. The answer is suppose to be to the nearest thousandth. The base of an 18-ft ladder is 4 ft away from a wall. How far above the floor is the      Log On


   

Question 109616: I need help with this problem please.
The answer is suppose to be to the nearest thousandth.
The base of an 18-ft ladder is 4 ft 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 4 with a hypotenuse of 18, 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%2B4%5E2=18%5E2 Plug in a=x, b=4, and c=18. Now lets solve for x


+x++%5E+2+%2B+1+6+=+3+2+4 Square each individual term



+x++%5E+2+=+3+2+4+-+1+6 Subtract 16 from both sides


+x++%5E+2+=+3+0+8 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+3+0+8+%29 Take the square root of both sides



x=2%2Asqrt%2877%29 Simplify the square root

Which approximates to...
x+=+1+7+.+5+4+9+9+2+8+7+7+4+7+8+4+2

So our answer is
x+=+1+7+.+5+4+9+9+2+8+7+7+4+7+8+4+2