Reading the question more carefully, I see I have misinterpreted the angles. The angle between incident and reflection is 45 degrees not 90 degrees, so we need to use the cosine rule:
a^2 = 100^2 + 120^2 - 2*100*120*cos(45°) where a is the distance between pocket and initial strike.
so a = sqrt(100^2 + 120^2 - 2*100*120*cos(45°))
a = 86 cm (to the nearest cm).