#1 Added by Nudge 3 years ago

. . . and some math.landmarks == flagsHow to locate A Ranger portal with just two measurementsYou thought that math in elementary school will never come handy?Here it is!You know there is a portal out there.You know that the Ranger map with the amber can tell you within 500 meters where the portal is.What it cannot tell you is what direction.I am going to show you how to figure this out with just two flags.You will need a piece of paper and pencil, and an arc-cosine table. Alternatively, you can use a spreadsheet like Microsoft Excel or LibreCalc;-)If we know the length of the three sides of a triangle, any shaped triangle, we can tell each and every angle of it using arc-cosine.The equation is as follows for each angle:Let's make the length of each side named a, b, and c, while name the angles A, B, and C.A=arccos(b^2+c^2-a^2 / 2bc)B=arccos(a^2+c^2-b^2 / 2ac)B=arccos(a^2+b^2-c^2 / 2ab)Let's put this into use to find the portal.Pull out your map, and let the amber search for the portal.Your first result is say 78. That means the portal is 78 meters away in any direction.Drop a flag and name the flag '78'.Now start out and travel towards any direction.Pull out your map, and let the amber search for the portal.The second result is 113. The portal now is 113 meters away, you went the wrong direction.Drop a flag and name it '113'. Do not move! If you moved off of the flag 113, move back to it until it is saying you are 0 meters away.Target the flag 78. How far is it? In our example, it is 169 meters away.Suddenly, now we have the three sides of the triangle.a=78b=113c=169Do not move! On your compass, right-click and select North. turn until you are facing North, as on the example. The white compass triangle points to the top.Now, use your elementary school calculation and get the angle for angle B, or the point that is connecting side b to side c.Put the numbers in your spreadsheet in cells A1, A2, and A3, respectively.In Excel/LibreCalc/OpenCalc the equation is:In C1 put the following equation. This calculates the angle for angle B, which is at the point where sides a and side c meet.=DEGREES(ACOS((A2^2+A3^2-A1^2)/(2*A2*A3)))My result for this angle is 33.92510046.... Which means nothing unless you have a protractor.Take a look at 34 degrees. It appears twice on the protractor, on the left of 90 and right of the 90 degrees.Since the other point is to the left of us, look at the left side.From look at North (90 degrees), the portal is 34 degrees, and 113 meters away.If we were at the left flag (flag 78), the calculation would be :=DEGREES(ACOS((sidea^2+sideb^2-sidec^2)/(2*sidea*sideb)))My result for that is 123.4160631. Since the other flag is to the right, the portal is 123 degrees, and 78 meters away.To make it into step actions:0. get closer than 500 meters to portal1. measure first distance sidea to portal2. create flag at current location. Name it the distance to the portal3. run somewhere else4. measure second distance sideb to portal5. measure distance to first, sidea flag, this is sidec6. look North6. calculate angle from current spot using sidea, sideb and sidec measurements =DEGREES(ACOS((sidea^2+sideb^2-sidec^2)/(2*sidea*sideb)))7. turn to calculated angle and run sideb meters8. read map again9. portal should be under youIn our example, purple flags are the measurement spots, and white flag is portal.

Hope this helps.

Edited 4 times | Last edited by Nudge (3 years ago)

#2 Added by Bitttymacod 3 years ago

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#3 Added by Nudge 3 years ago

There is one small problem with your analysis.There are actually two points that satisfy all the conditions you specify. They are on either side of the line between A and B.(Specifically the defined triangle can be flipped along the A-B line.)It's usually enough to look at the two locations and realize that solution #2 is in an aggro pile and look at the other one. :DIf you find a third point you can get a unique solution. I tend to just target point B, estimate where I'm going to end up (based on my eyeballs on the map, then run until the distance to point B is the right number, then target point A, and iteratively adjust my distances until I'm there, but that's just because I'm too lazy to do the maths.

#4 Added by Gidget 3 years ago

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