Question

15 foot ladder is leaning against a wall if the base of the ladder is 5 feet from the wall how high up the wall the ladder reach?

Answer 1

This is a good example of which Pythagoras's theorem could be used on.
The theorem states: a^2 + b^2 = c^2

If we subsitute the values into the question we get this:
a^2 + 5^2 = 15^2

Simplfy:
a^2 + 25 = 125

Then inverse:
125 - 25 = a^2

Answer it:
100 = a^2

Square root it:
10 = a

The answer is 10 feet
Hope it helped :)

Answer 2

The Pythagorean Theorem (
`a^(2) + b^(2) = c^(2)`) can be used to solve this problem.
We know that the ladder is 15 feet in length, and is leaning on a wall from 5 feet away. To work this out, we simply need to figure out which side is the hypotenuse.
The hypotenuse of a right triangle is always the side opposite of the right (90°) angle. In this case, the right angle is that which is made at the wall's intersection with the ground.
In the Pythagorean Theorem, c represents the length of the hypotenuse.

So now, we can work out this problem substituting what we know into the theorem.


`(a^(2) + b^(2) = c^(2)) = (c^(2) - a^(2) = b^(2))`


`15^(2) -5^(2) = b^(2)`


`225 - 25 = b^(2)`


`200 = b^(2)`

So now we have the result for
`b^(2)`. Since 200 isn't a perfect square, we can represent the length of b as
`√(200)` which is our answer.

The ladder reaches
`√(200)` feet up the wall.
Hope that helped! =)