Pythagorean theorem word problems arise in numerous situations. We will cover a couple a solid examples here.

John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?

Here is how you can model this situation

Let c be the missing distance from school to home and a = 6 and b = 8

c

c

c

c

c = √100

c = 10

The distance from school to home is 10 blocks.

A 13 feet ladder is placed 5 feet away from a wall. The distance from the ground straight up to the top of the wall is 13 feet Will the ladder the top of the wall?

c

13

169 = 25 + b

169 - 25 = 25 - 25 + b

144 = 0 + b

144 = b

b = √144 = 12

The ladder will never reach the top since it will only reach 12 feet high from the ground yet the top is 14 feet high.