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:
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
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229 miles N __
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__
St. Louis
That direct line is the hypotenuse of a right triangle. We can calculate this distance using the pythagorean theorem:
a^{2} + b^{2} = c^{2}
or
229^{2} + 136^{2} = c^{2}
52,441 + 18,496 = c^{2}
70,937 = c^{2}
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.