Hello mathematicians
A friend and I tried to figure this out for a while. We tried a lot, but could not find anything.
We have two given points (A and B)
Two given lengths ($\overline{AB}$ = $\overline{BC}$)
One given corner ($\alpha$)
We want to find a general formula for the coordinates of C.
We basicly want the formula to be valid for any angle, with any coordinates, with any length.
I hope someone can help us out, we think we are looking over something.
Since is a isosceles triangle, and $AB = BC$, you know that $By = Cy$. Because $AB$ and $BC$ have the same length. If you cut the Triangle in two parts you can see that it forms two right triangle.
Now, how to find $Cx$. Well $|Cx - Bx| = BC$ Becausa in a plane, the distance between two points (In the same axis, this case, x) $A$ and $B$ is $|A - B|$ which is the same that $|B - A|$