SOLUTION: I have the following homework problem I can not seem to fit into one of the provided answers: A 13-ft ladder is leaning against a building. The bottom of the ladder is 5 ft fro

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Question 110946: I have the following homework problem I can not seem to fit into one of the provided answers:
A 13-ft ladder is leaning against a building. The bottom of the ladder is 5 ft from the building. How high is the top of the ladder?
sq rt of 18ft
sq rt of 8ft
12 ft
sq rt of 194ft
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 13, 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=13%5E2 Plug in a=x, b=5, and c=13. Now lets solve for x


+x++%5E+2+%2B+2+5+=+1+6+9 Square each individual term



+x++%5E+2+=+1+6+9+-+2+5 Subtract 25 from both sides


+x++%5E+2+=+1+4+4 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+1+4+4+%29 Take the square root of both sides



x=12 Simplify the square root


So the ladder touches the 12 ft mark on the building