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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.

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1 Answer

Hi Tiphany-
Here is how to solve this problem:
 
First, let's start with a drawing to visually represent the information:
 
    |---------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.