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?

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)   (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 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.

Since the legs are and this means that and

Also, since the hypotenuse is , this means that .

Start with the Pythagorean theorem.

Plug in , ,

Square to get .

Square to get .

Subtract from both sides.

Combine like terms.

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

Simplify the square root.

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Answer:

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

Answer by nerdybill(7384)   (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)   (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.
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