Here, we have light moving from vacuum into transparent plastic. The angle of incidence is 72.7 degrees and the angle of refraction is 57.1 degrees. As the refractive indexes of vacuum and plastic are different, light moves at a different speed in plastic than it does in vacuum.
The relation between the speed of light in vacuum vc, the speed of light in the plastic vp, the angle of incidence Ai and angle of refraction Ar is given by:
sin Ai / sin Ar = vc / vp
=> sin 72.7 / sin 57.1 = vc / vp
=> vp = vc * (sin 57.1/ sin 72.7)
=> vp = vc * 0.8794
The speed of light in vacuum is 3*10^8 m/s. The speed of light in the plastic is 2.63*10^8 m/s
The required speed of light is 2.63* 10^8 m/s.