Final answer:
The magnitude of static friction force is equal to the applied force, which is 137 N, because the box remains stationary.
Step-by-step explanation:
The question is about determining the magnitude of the static friction force when a boy exerts a horizontal force on a box that remains stationary. Since the box doesn't move, we can infer that the static frictional force has to be equal to the applied force to prevent motion, given that there are no other horizontal forces acting on the box.
In this case, the boy is exerting a force of 137 N, and since the box remains at rest, the static frictional force must be countering this force completely. So, the correct answer is (a) 137 N.