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# Chicago is located 229 miles north and 136 miles east of St Louis. What is the direct distance between Chicago and St Louis? Round to nearest tenth of a mile.

Chicago is located 229 miles north and 136 miles east of st Louis. What is the direct distance between Chicago and St Louis? Round to the nearest tenth of a mile.

Hi Tiphany-
Here is how to solve this problem:

|---------136 miles E----- Chicago
|
|
229 miles N
|
|
St. Louis

Now, the key to solving this problem is recognizing two things: (1) you need the exact distance from St. Louis to Chicago which is a straight line, and (2) once you draw in the line, it creates a right triangle:

|---------136 miles E----- Chicago
|                            __---
|                     __---
229 miles N      __---
|       __---
|__---
St. Louis

That direct line is the hypotenuse of a right triangle.  We can calculate this distance using the pythagorean theorem:

a2 + b2 = c2
or
2292 + 1362 = c2

52,441 + 18,496 = c2
70,937 = c2

Now take the square root of both sides to get:

266.34 = c

Therefore, the distance between Chicago and St. Louis is 266.34 miles.