Idiot\'s Guides Basic Math and Pre-Algebra

174 Part 3: The Shape of the World

DEFINITION

The Pythagorean theorem states that for any right triangle, the square of the

hypotenuse is equal to the sum of the squares of the other two sides, or if the length

of the hypotenuse is c, and the lengths of the legs are a and b, then a^2 + b^2 = c^2.

The importance of the Pythagorean theorem comes from the fact that you can use it to find the

length of one side of the right triangle if you know the other two.

Suppose 'RST is a right triangle with right angle at R. If RS = 7 and RT = 4, you can find the

length of side TS with the Pythagorean theorem. The right angle is at R, so the sides you know

are the legs that make the right angle, and you’re looking for the hypotenuse. Use a^2 + b^2 = c^2 ,

with a = 7 and b = 4.

c^2 = 49 + 16

c^2 = 65

This means TS will be^65 , which is slightly more than 8.06.

You’ve probably thought about problems that could be solved with the Pythagorean theorem.

Here’s one. Elise walks to school every morning, and on sunny days, she can cut across the

football field from corner to corner. On snowy days, she must go around the outside edges of the

field. How much shorter is Elise’s walk on sunny days?

The field has a right angle at its corner, and Elise’s path from corner to corner makes the

hypotenuse of a right triangle. The field, including the end zones, is 120 yards long and 53.33

yards wide. Use a^2 + b^2 = c^2 , with a = 120 and b = 53.33 to find the length of Elise’s shortcut.

On sunny days, Elise can take the shortcut that’s about 131.32 yards, but on snowy mornings,

she’ll have to go around the edges of the field, a total of 120 + 53.33 = 173.33 yards. On sunny

days, she saves 173.33 – 131.32 } 42.01 yards. Her sunny day route is about 42 yards shorter.

cab

c

c

c

222

2 22

2

2

120 53.33

14,400 2,844.0889

17,244.0889

17,244.0889

131.32

c

c