SOLUTION: Construction. The base of a 15-ft ladder is 5-ft away from a wall. How far above the floor is the top of the ladder? I set up using the formula of {{{5^2+h^2=15^2}}} Am I corre

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Construction. The base of a 15-ft ladder is 5-ft away from a wall. How far above the floor is the top of the ladder? I set up using the formula of {{{5^2+h^2=15^2}}} Am I corre      Log On


   

Question 280791: Construction. The base of a 15-ft ladder is 5-ft away from a wall. How far above the floor is the top of the ladder?
I set up using the formula of 5%5E2%2Bh%5E2=15%5E2
Am I correct in this set up? I am also having issues solving it, Thank you very much for your help!
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 5 and h this means that a=5 and b=h


Also, since the hypotenuse is 15, this means that c=15.


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


5%5E2%2Bh%5E2=15%5E2 Plug in a=5, b=h, c=15


25%2Bh%5E2=15%5E2 Square 5 to get 25.


25%2Bh%5E2=225 Square 15 to get 225.


h%5E2=225-25 Subtract 25 from both sides.


h%5E2=200 Combine like terms.


h=sqrt%28200%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


h=10%2Asqrt%282%29 Simplify the square root.


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Answer:


So the solution is h=10%2Asqrt%282%29 which approximates to h=14.142 (using a calculator).


So the top of the ladder is approximately 14.142 ft above the floor.