# How To Project A Third Point To Form A Triangle

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I am trying to solve a geocache in which the posting makes known two co-ordinates and expects the cacher to project a third co-ordinate that forms an equal sided triangle. Is there a way to mathmatically find the exact co-ordinate?

Any help?

thanks,

wildthing

take that distance from a to b . since angles of a triangle =180 check your heading from a to b , add or subtract 60 and head in that direction = to a-b

does this make sense? it does in my head

steve

This is how the only person to find the cache found it. It sort of makes sense to me. I didn't note the distance from point to point when I was actually at the waypoints. I am trying to figure it from my home and just go to the third point (where the cache is hidden). I may have to drive out to the locations and try this method, though.

thanks

are we talking miles or feet apart?

steve

It is aprox. 3.8 miles apart.

Did you put the waypoints on your GPSr? On my eTrex Vista I can measure distances between waypoints.

I did this at home one time for a friend's property corners and got it right within about 8 feet.

I am trying to solve a geocache in which the posting makes known two co-ordinates and expects the cacher to project a third co-ordinate that forms an equal sided triangle. Is there a way to mathmatically find the exact co-ordinate?

Any help?

thanks,

wildthing

I love doing this.. I use Delorme Topo Usa and it has a draw feature. In put what you know and draw the other legs of the triangle. Works Great!!

Can you give me the cache Location??? I will try it.

N41deg 25.392

W093deg 05.282

I realize the third point could go either northwest or southeast from this line, but I am pretty sure, by the area it is in, the likely hidding spot would be southeast.

John

I worked on a cache like this, difference was the sides of the triangle where not the same. What I did was put both known waypoints on Mapsource. I did not know the distance to the 3rd waypoint, just heading. So I did a waypoint projection out a distance that I figured was further then the 3rd waypoint. I did this from both known points, then moved the cursor to where the projections crossed and read the coords at the bottom of Mapsource.

Al

N41deg 25.392

W093deg 05.282

I realize the third point could go either northwest or southeast from this line, but I am pretty sure, by the area it is in, the likely hidding spot would be southeast.

John

Can you give the cache page?? Link and where is the other point??

This location is on the edge of a lake near Pella

Edited by wingnuts

Use UTM coordinates. They also should have given you a way to tell which side of the triangle to solve.

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Either side of the baseline (the coords you were given) can solve a triangle unless you have more information.

Equilateral triangles have a few tricks that make them easier to solve.

opps sorry, I did mean to give two locations. They are :

N41deg 27.653

W93deg 02.087

AND

N41deg 25.392

W93deg 05.282

N41deg 25.392

W093deg 05.282

I realize the third point could go either northwest or southeast from this line, but I am pretty sure, by the area it is in, the likely hidding spot would be southeast.

John

Can you give the cache page?? Link and where is the other point??

This location is on the edge of a lake near Pella

Red Rock Challenge cache is the one you are working on?? give me a few min.

yep, that is it.

yep, that is it.

It would appear that this is not that much of a Triangulation cache?? As it requires knowledge of the surrounding area. This cache "Triangulation Cache" in south east MI is more as you described.

After reading the clues 942' I thought of the near by obsevation tower?? but it doesn't fall into the distances described 3.5 miles.

It appears that the elevation in a 3.5 mile circle is less than 942' so that being said is their any other structures in the area that would give you that elevation?

The clue "See history, fourty-six" sounds like a point of interest on a visitors map of the area??

I would do this...

Use the lat. and lon. given as point one.

Go to the top of the obsevation tower in the same park see if you elevation is 942'.. if it is.

Look for "Sight the unadorned twin" in the distance about 3.5 miles (See history, fourty-six.. check if their is some guide map in the tower as to what you are looking at that has 46 as its id) this would be your second point in the triangle.

This might get you started. If what I suggest helps and you can give be an accurate second lat. and lon. I can try to further help out.

I am pretty sure I got it figured out. Nice day for a drive so I am heading out to locate the cache. I have used Mapsource combined with Expert GPS and I think I am on to it. I will let you know.

I am pretty sure I got it figured out. Nice day for a drive so I am heading out to locate the cache. I have used Mapsource combined with Expert GPS and I think I am on to it. I will let you know.

cool post back here as to how you found it...

Beautiful area! Maybe you can do both of us a favor - when I was in Pella a couple of years ago I fished the tailwaters below Red Rock Dam (under the spillway was the only thawed water - it was -7° and the lake and river were frozen solid!), and that evening ate at a really cool restaraunt whose name I can't remember!

Mayby you can find it and let me know the name, and have a fun meal while you're at it!

It was s steakhouse unlike any I have ever seen - on one wall they had a meat case where you selected your meat of choice, a salad bar, drink cooler and a baked potato oven. The other wall was one long charcoal pit - you got the cut of meat you wanted and took it to the pit and stood around and cooked your own dinner, sharing a drink and talking to all the other diners while they cooked theirs!

I have never seen a place like it, loved it, and am seriously interested in opening such a restaraunt here in Alabama. If you find it, have a great meal and let me know!

I tend to attack this kind of puzzle with brute force using Excel. I build a sheet with the points which I know (use decimal degrees, dd.ddddd) and a guess of the one I don't. Then I have cells showing the error with respect to each known cell, and another one which is the MAX() of these. (I use 1852 metres for a minute of latitude and (1852*cos(latitude) metres) for a minute of longitude. Don't forget to use the RADIANS() function in Excel, if you input the coordinates in degrees.)

Then all you have to do is vary the initial guess a bit. First you add, say, 0.01 to the N of the guess and see if the MAX() error goes up or down. If it goes up, subtract 0.1 instead. Continue subtracting until the error goes up. Now repeat with the E coordinate, then continue changing N, E, N, E, by smaller amounts each time. When the MAX() error is about one foot, you won't do much better on the ground...

Of course, it's better to do it trigonometrically, but this way always works, even when you can't remember the offiicial way to do it.

It was s steakhouse unlike any I have ever seen - on one wall they had a meat case where you selected your meat of choice, a salad bar, drink cooler and a baked potato oven. The other wall was one long charcoal pit - you got the cut of meat you wanted and took it to the pit and stood around and cooked your own dinner, sharing a drink and talking to all the other diners while they cooked theirs!

That reminds me I was in E.Moline Il for a class and went to one like this loved it thought it was a great idea, I have heard of one in Panama City or Pensacola which I'm not sure.

Wildthings I see from your post on the cache site you had a DNF on this cache.. any new info??

Edited by wingnuts

This is another problem that can be easily solved using your GPSr and nothing else. You can do it in the field or anyone can do it where ever they are. When I get home I will do this and post an answer.

1. Enter both coords as waypoints.

2. Create a route with First waypoint and Second. Note the distance and bearing from the first to the second.

3. Go to your Projection (Project a waypoint) page. For distance, put in the distance from First to Second (since all three sides on this triangle are equal.) For bearing, take the bearing from above and add 60 degrees(all three angles are 60.) The projection will now give you the waypoint of the third point in the triangle.

4. Do another projection, this time subtract 60 degrees. This will give you the waypoint of the third point of the triangle on the opposite side.

You may want to use mils for more precision. Your adjustment is then 1066.67 mils.

Here's another easy way, at least with a Garmin. Create a proximity alarm zone centered on each waypoint, with the radius equal to the distance between the points. The two proximity circles will touch at two points; one of those will be your cache.

I did the projection with my Meridian, which has an excellent projection tool. Entering the 2 coords as waypoints and dropping them into a route, the most southwesterly WP shows 3.79 miles and 47 degrees True to the second. I used Kilometers (6.10 KM) and mils (829 mils) because you get more precision. Projecting from the first WP 6.10KM at 1,895.67 mils (829+1067.67) gives you your Cachepoint (you said it was the triangle SE of the 2 WPs.)

Projecting from the second WP (the Northeasterly one) as a check, 6.10KM at 2,962.33 mils, gives a Cachepoint 2 thousandths of a minute in Long. from the first calculation (within 10 feet.)

It only takes a couple of minutes to do this. I will not post the Cachepoint coords since the cache was named.

There are 6400 mils in a circle, compared to 360 degrees. Each angle of a equallateral triangle is 60 degrees which equals 1,067.67 mils.

Yes, I did finally find the cache! Three tries and I had to ask to owner for another hint. The coordinates I came up with were correct, but needed a little more direction than I got from the posted hints. I used Mapsource software to help me with this. Also so ideas from some of the posts. Thanks for all your help.

Not to be a part pooper, but its in kind of poor taste to ask for help on a puzzle cache in the forums. The cache owher obviously put alot of thought and work into the cache and would probably not be too happy if others were spoiling it on them.

Not to be a part pooper, but its in kind of poor taste to ask for help on a puzzle cache in the forums. ...

In general, I agree, but in this case the question was just about a mathematical method--not a request for a nudge on the particular cache. I think that's probably acceptable.

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