In the real world I have 3 points of interest ABC. A B and C are each 20 cm apart and are placed in a equilateral triangle formation.
A coordinates are (-10, 0) and C coordinates are (10, 0). I'm using these points to show the distance and I will form hyperbolas between each of these points and wish to know where intersection occurs.
What coordinates do I plot B in relation to A and C. Would I find 60 degrees from A (-10,0) and see where it intersects the Y axis. Would it be at (0, 10), (0, 20) or something else, I'm quite confused how this would work.
You have an equilateral triangle, ABC, and points A and C are (-10, 0) and (10, 0) respectively. You appear to know that B will lie directly above the midpoint of AC so the x coordinate of B is 0. Now imagine drawing a line from B to that midpoint. D. That divides the equilateral triangle into two right triangles, ABD and CBD. The distance from A to C is 20 so AB and CB, the hypotenuses of the right triangles, are also 20. AD and CD, legs of the two right triangles, are 20/2= 10. By the Pythagorean theorem, h, the y coordinate of B, satisfies $h^2+ 10^2= 20^2$ so $h^2= 400- 100= 300$. $h= \sqrt{300}= 10\sqrt{3}$ so B has coordinates $(0, 10\sqrt{3})$.