Answer
$29mH$
Work Step by Step
We can find the required inductance as follows:
$Z=\frac{R}{cos\phi}$
$Z=\frac{2.7}{cos76^{\circ}}=11.6\Omega$
We know that
$Z=\sqrt{R^2_+(\omega L)^2}$
This simplifies to:
$L=\frac{\sqrt{Z^2-R^2}}{\omega}$
$\implies L=\sqrt{\frac{(11.16)^2-(2.7)^2}{2\pi (60.0)}}$
$L=29mH$
