Well, I think you have to use the Law of Sines. First we need to know at what height of the mirror the beam strikes, so using the law of sines you get

sin(56.3)/1.10 = sin(33.7)/x1

where x1 is the height at which the beam strikes.

solving for x1=(1.10)(sin(33.7))/sin(56.3)=0.73

Now we can apply the law of sines to know how far from the base of the mirror does the beam strike the floor, lets call that x2.

sin(33.7)/1.07=sin(56.3)/x2

Solving for x2,

x2=(1.07)(sin(56.3))/sin(33.7)=1.60

So the final answer is 1.60 m. All the angles are in degrees