Ship's Bearing

Date: 8/22/96 at 13:7:3
From: Anonymous
Subject: Bearing of a Ship

A ship travels 8km due east and then 8km due north. What is the 
bearing of the ship from its initial point?

Date: 8/22/96 at 14:20:1
From: Doctor Paul
Subject: Re: Bearing of a Ship

the ship goes 8 km to the right and then 8 km up:

         
           /|
          / |
         /  |
        / b |
       /    | 
   x  /     |
     /      |
    /       |
   /        | 8 km
  /         |
 / a      c |
 -----------    ----->  due east!
    8 km


You want to solve for the distance x.  In this situation, we know 
that the two sides are the same length so we know that a and b are 
45 degrees, while c is 90 degrees.  

In a 45,45,90 triangle, the length of the hypotenuse is the length of 
the side times the square root of two.

So the distance x = 8*sqrt(2) = 11.314

and the bearing is 11.314 km at 45 degrees north of east.

I hope this helps clear things up.

-Doctor Paul,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/