Simple phasor problem with AC
You are correct that the resistor current and capacitor current are out of phase by 90 degrees, but in your solution you assumed that the total current and the capacitor current are out of phase by 90 degrees.

The current through \$A_1\$ is the total current and the current through \$A_2\$ is 90 degrees out of phase with the resistor current. If you draw the phase diagram \$A_1\$ is the hypotenuse. Can you use geometry and take it from there?