Question 867354
let the third vertex be A
A(x,y), B(0,0) C(10,0)

distance AB=BC=CA =10( equlateral triangle)

distance formula
{{{d= sqrt ((x1-x2)^2+(y1-y2)^2)}}}

{{{d^2=((x1-x2)^2+(y1-y2)^2)}}}

AB = x^2-y^2
AC=(x-10)^2+y2 
AB=AC

x^2-y^2=(x-10)^2+y2
x^2+y^2=(x^2-20x+100+y2)

20x=100
x=5
Plug x
x^2+y^2=100
25+y^2=100

y^2=75
y=+/-5sqrt(3)

A (x,5sqrt(3)) , (5,-5sqrt(3))