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### 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/
```
Associated Topics:
Middle School Geometry
Middle School Triangles and Other Polygons

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