SOLUTION: A 28 ft. ladder is leaning halfway up a 40 foot building. How far from the building should ladder be placed? (Round answer to the nearest foot)

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Question 360748: A 28 ft. ladder is leaning halfway up a 40 foot building. How far from the building should ladder be placed? (Round answer to the nearest foot)
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 20 and x this means that a=20 and b=x


Also, since the hypotenuse is 28, this means that c=28.


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


20%5E2%2Bx%5E2=28%5E2 Plug in a=20, b=x, c=28


400%2Bx%5E2=28%5E2 Square 20 to get 400.


400%2Bx%5E2=784 Square 28 to get 784.


x%5E2=784-400 Subtract 400 from both sides.


x%5E2=384 Combine like terms.


x=sqrt%28384%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=8%2Asqrt%286%29 Simplify the square root.


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Answer:


So the solution is x=8%2Asqrt%286%29 which approximates to x=19.596.


So the ladder should be placed approximately 20 ft from the building (rounded to the nearest foot).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim