Will it reach a window that is 10 ft up? How do you know?

Question

The bottom of a 13 ft ladder is placed 5ft away from the side of a house.

Answer 1

What we have here is a Pythagorean theorem problem:
a2 + b2 = c2
We have both sides and the possible hypotenuse, so we just need to put our values in:
102 + 52 ≤ 132
 
We're using a less or equals sign because we want to know if it can reach.
100 + 25 ≤ 169
125 ≤ 169
 
So yes, the ladder will reach the window.

The case can also be made that since the theorem shows the added squared lengths being much shorter than the squared hypotenuse, that the ladder will overshoot the window.