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?

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) (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).

Take the square root of 576 to get 24.

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Answer:

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

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