If you analyze the forces acting on the roof, then
Frictional force = F = mg(sin Θ)
where
F = 430 N (given)
m = mass of the worker
g = acceleration due to gravity = 9.8 m/sec^2 (constant)
Θ = 23 degrees (given)
Hence, substituting appropriate values in the above equation,
430 = (m)(9.8)(sin 23)
and solving for "m"
m = 112 kg.
Hope this helps.
