SOLUTION: A ladder that is 26 feet long is 10 feet from the base of a wall. How far up the wall does the ladder reach?

Algebra ->  Pythagorean-theorem -> SOLUTION: A ladder that is 26 feet long is 10 feet from the base of a wall. How far up the wall does the ladder reach?      Log On


   

Question 293359: A ladder that is 26 feet long is 10 feet from the base of a wall. How far up the wall does the ladder reach?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are x and 10 this means that a=x and b=10


Also, since the hypotenuse is 26, this means that c=26.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


x%5E2%2B10%5E2=26%5E2 Plug in a=x, b=10, c=26


x%5E2%2B100=26%5E2 Square 10 to get 100.


x%5E2%2B100=676 Square 26 to get 676.


x%5E2=676-100 Subtract 100 from both sides.


x%5E2=576 Combine like terms.


x=sqrt%28576%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=24 Take the square root of 576 to get 24.


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Answer:


So the solution is x=24 which means that the ladder reaches 24 ft up the wall.