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.

Question

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.

Answer 1

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.