Answer
$\phi = 82.8^{\circ}$
Work Step by Step
The amplitude of the resulting wave is $~~2y_m cos \frac{\phi}{2}$
We can find the phase difference $\phi$:
$2y_m cos \frac{\phi}{2} = 1.5~y_m$
$cos \frac{\phi}{2} = \frac{1.5}{2}$
$\frac{\phi}{2} = cos^{-1} (\frac{1.5}{2})$
$\phi = 2~cos^{-1} (\frac{1.5}{2})$
$\phi = (2)(41.4^{\circ})$
$\phi = 82.8^{\circ}$
