SOLUTION: A 13 foot ladder is leaned against a wall so that the ladder reaches a height of 12 feet on the wall. How far from the wall will the other end of the ladder be?

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Question 281608: A 13 foot ladder is leaned against a wall so that the ladder reaches a height of 12 feet on the wall. How far from the wall will the other end of the ladder be?
Found 3 solutions by jim_thompson5910, nerdybill, richwmiller:
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 12 this means that a=x and b=12


Also, since the hypotenuse is 13, this means that c=13.


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


x%5E2%2B12%5E2=13%5E2 Plug in a=x, b=12, c=13


x%5E2%2B144=13%5E2 Square 12 to get 144.


x%5E2%2B144=169 Square 13 to get 169.


x%5E2=169-144 Subtract 144 from both sides.


x%5E2=25 Combine like terms.


x=sqrt%2825%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=5 Simplify the square root.


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Answer:


So the solution is x=5 which means that the foot of the ladder is 5 ft from the base of the wall.

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
A 13 foot ladder is leaned against a wall so that the ladder reaches a height of 12 feet on the wall. How far from the wall will the other end of the ladder be?
.
The ladder, wall and floor forms a right triangle (triangle with a 90 deg angle). Thus, we can apply the Pythagorean theorem:
Let x = distance from wall
then
x^2 + 12^2 = 13^2
x^2 + 144 = 169
x^2 = 169 - 144
x^2 = 25
x = 5 feet

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+12^2=13^2
This is a pythagorean triplet that you should know
5,12, 13 right triangle.
answer 5 ft.