Hello,
The typical way to find a stronghold is to essentially brute force your way there; stock up on Eye of Enders, then throw and follow until your eye sinks into the ground. While this may be quick it is not very cost-effective, especially if, like me, you like to play on hardcore mode where Enderman will wreck you fast. This guide will explain how to very quickly find a stronghold in a new world, using only 3 (or even just 2) Eyes and some trigonometry/geometry.
Step 1: Find somewhere spacious and relatively flat. Deserts, plains, ice plains, even oceans are suitable. Pick any spot and record your coordinates. The Y coordinate is irrelevant.
Step 2: Toss an Eye. Do not move from your spot and follow the eye with your mouse. As the eye stops and hovers, place your reticle as close to the center of that eye as possible, and then let go of your mouse so as to hold your position. Record your facing angle (example below)
Step 3: Move to a new spot by only moving along either the x axis or z axis (one of those values should remain the same) by a predetermined amount. It's best to move as close to orthogonal from your current facing as possible (I'll explain in an example later). I've found that you need to move at least 200m away from the first position, and move away no further than 1km. Record this new position.
Step 4: Toss another eye just as before and record your new angle.
Step 5: Math time. We will be using the
law of sines:
to calculate the distance from point 1 to the stronghold. The equation is as follows:
d1= L * sin(angle1) / sin(angle3)
Where d1 is the distance from point 1 to the stronghold, L is the distance between point 1 and point 2, angle1 is the interior angle between d1 and L, and angle3 is the interior angle between d1 and d2.
Step 6: Math continued. Now that we have the distance, we need to break it up into its x and z coordinates so that we can determine the absolute location of the stronghold. For the x component:
dx = d1 * -sin(angle)
To find the z component:
dz = d1 * cos(angle)
Where angle is the literal angle you recorded on your first throw.
Step 7: Last math thing. Now that you have your x and z components of that distance, add those values to your initial location coordinates. The result is the coordinates of the stronghold. Simply walk there and confirm its location with your final eye.
I realize that the math can be a bit confusing for those not familiar with trigonometry, so I'll provide an example:
1st Location: X = 0, Z = 0
1st angle: 100.06
2nd Location: X = 0, Z = 200
2nd angle: 113.86
I chose to move along the z axis here, because the z axis points in both 0 and 180 degrees, which is close to orthogonal from the first angle. If I had moved in the X axis' direction, I would be subject to a large margin of error.
L = 200m
angle1 = 100.06 deg
angle2 = 180 - 113.86 = 66.14 deg
angle3 = 180 - angle1 - angle2 = 13.8 deg
d1 = 200 * sin(100.6) / sin(13.
= 825.57m
dx = -812.87m
dz = -144.21m
Final coordinates:
x = -812.87
z = -144.21
Upon looking, the actual coordinates for the stronghold were at:
z = -744
x = -161
So as you can see, there is still some error even at L = 200. Increasing this L will increase its opposite angle which will in turn lessen the amount of error you get. But either case, this is much cheaper than the brute force method, which was the goal.
I'm not terribly good at explaining things, so feel free to comment with questions. If you feel the math is too hard, just drop in your 4 recorded values (2 locations, 2 angles) and I'll pump out some coordinates for you. Thanks for reading.
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