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?

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 :)

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CmdrWinters CmdrWinters · Answer 2 · 2016-05-23T23:43:37+02:00

The Pythagorean Theorem ([tex] a^{2} + b^{2} = c^{2} [/tex]) 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.

[tex](a^{2} + b^{2} = c^{2}) = (c^{2} - a^{2} = b^{2})[/tex]

[tex]15^{2} -5^{2} = b^{2} [/tex]

[tex]225 - 25 = b^{2} [/tex]

[tex]200 = b^{2} [/tex]

So now we have the result for [tex]b^{2} [/tex]. Since 200 isn't a perfect square, we can represent the length of b as [tex] \sqrt{200} [/tex] which is our answer.

The ladder reaches [tex] \sqrt{200} [/tex] feet up the wall.
Hope that helped! =)