# Projected waypoint

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A projected waypoint is where a second waypoint is a given bearing and distance from a given waypoint. Many GPS receivers can perform this calculation but for those that don't, here is how to manually calculate the second location. And by manually we mean with a trigonometic table book or slide rule, pen and paper.
i.e. Your Laptop, PDA, mobile phone and calculator have flat batteries leaving only the GPSr working.

Assumptions:
This will only work for a few kilometers but should be fine for caching. I'm assuming you are in Australia.
A book with sines and cosines or a slide rule and the ability to perform simple maths without a calculator!
You have printed this out and put it in your Geocaching folder!

Given:
Sorig is the first southing in the form dd mm.mmm
Eorig is the first easting in the form dd mm.mmm
D is the distance from location one to the second location in metres.
B is the bearing from location two to the second location in degrees.
S is the southing in the form DD.DDDDD, calculated from Sorig

Solution:
First lets calculate the distance in the southing and easting to the second location in metres.
deltaS = -D * cos(B)
deltaE = D * sin(B)

Now we need to convert this distance in metres to minutes of latitude and longitude.
deltaSmin = deltaS / 1853
deltaEmin = deltaE / (1853 *cos(S))

These are the variations to the minutes in the form mm.mmm
This is based on 1 minute of latitude 1nm. (1nm = 1853m)
The deltaEmin takes into account as you move towards the poles 1 minute of longitude gets smaller.

Snew = Sorig + deltaSmin
Enew = Eorig + deltaEmin

Example
Sorig S34 46.533
Eorig E138 36.090
D 800m
B 25 degrees
therefore S is 34.77555, cos(S) = 0.821

deltaS = -800 * cos(25)

```      = -800 * 0.9063
= -725m
```

deltaE = 800 * sin(25)

```      = 800 * 0.4226
= 338m
```

deltaSmin = -725 / 1853

```         = -0.391
```

deltaEmin = 338 / (1853 * 0.821)

```         = 0.222
```

Snew = S34 46.533 - 0.391

```    = S34 46.142
```

Enew = E138 36.090 + 0.222

```    = E138 36.312
```