What are the coordinates?

Since it is equilateral, we know CAB is 60 degrees. To find the incentre, we bisect that angle, giving us a 30 degree angle at CAD. We also know AC is 4 units long. We can realize easily that AD is congruent to CD by ASA, therefore ADC will be 120 degrees. We can solve for AD using the law of sines: $\frac{sin(120)}{4}=\frac{sin(30)}{\overline{AD}}$ $\overline{AD}=\frac{4\cdot sin(30)}{sin(120)}\approx 2.31$ We now have the polar coordinates: (2.31, 30) which we can convert into Cartesian coordinates: $x=cos(30) 2.31 = 2$ $y=sin(30) 2.31\approx 1.1547$ . Rounding to nearest hundredths, $\boxed{1.15}$ .