Pythagorean theorem word problems

Pythagorean theorem word problems arise in numerous situations

Pythagorean problem # 1

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

East-west-north-south-image

The distance from school to home is the length of the hypotenuse.

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

c² = a² + b²

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = √100

c = 10

The distance from school to home is 10 blocks.

Pythagorean problem # 2

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?

East-west-north-south-image

Let the length of the ladder represents the length of the hypotenuse or c = 13 and a = 5 the distance from the ladder to the wall.

c² = a² + b²

13² = 5² + b²

169 = 25 + b²

169 - 25 = 25 - 25 + b² (minus 25 from both sides to isolate b² )

144 = 0 + b²

144 = b²

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.