Calculating inductance and resistance of a coil from current and voltage
There is a fault in your problem. If the total supply voltage is 240 volts then this is made up from the resistor voltage and the inductor voltage in series and in quadrature i.e.: -

Vtotal = \$\sqrt{V_R^2+V_L^2}\$ = \$\sqrt{90^2+180^2}\$ = 201.2 volts

This is not 240 volts so the problem in your question is flawed.