Answer
$\phi = 42.0^{\circ}$
Work Step by Step
Note that the light ray reflects off the mirror at the same angle as it strikes the mirror.
Thus the angle between the surface of the mirror and the incident ray is $\phi$, and the angle between the surface of the mirror and the reflected ray is $\phi$
Let $x$ be the distance from the top left corner where the ray should strike the mirror.
We can use similar triangles to find $x$:
$\frac{x}{3.00~m} = \frac{5.00~m-x}{1.50~m}$
$1.50x = 15.0-3.00x$
$4.50x = 15.0$
$x = \frac{15.0}{4.50}$
$x = 3.33~m$
We can find $\phi$:
$tan~\phi = \frac{3.00~m}{3.33~m}$
$tan~\phi = 0.90$
$\phi = tan^{-1}~(0.90)$
$\phi = 42.0^{\circ}$
