# Geometry/Chapter 15

If you understand the Pythagorean Theorem and what it derives from, you can now start applying its formula to everyday problems.

## Examples

### Example 1 - Plane Distance

A plane flies south from an airport at 300 miles per hour. Another plane flies out at the same time due east at 250 miles per hour. How far apart are the planes after three hours?

### Solution to Example 1

The solution would be about 1172 miles apart after three hours. How do we determine the answer?

 ${\displaystyle a^{2}+b^{2}=c^{2}}$                          The Pythagorean Theorem.
${\displaystyle (300*3)^{2}+(250*3)^{2}=c^{2}}$                Substituting miles per hour.
${\displaystyle 900^{2}+750^{2}=c^{2}}$                       Simplifying.
${\displaystyle 810000+562500=c^{2}}$                   Simplifying.
${\displaystyle {\sqrt {c^{2}}}={\sqrt {810000+562500}}}$      Finding the hypotenuse (or distance).
${\displaystyle c={\sqrt {1372500}}}$ or ${\displaystyle c\approx 1172}$     Our distance, simplified.