Force equilibrium and resolution Steps: - Vertical forces balance: vertical component of tension equals weight, so T cos θ = W. - Horizontal forces balance: horizontal component of tension equals push, so T sin θ = P. - Square and add components: (T cos θ)² + (T sin θ)² = W² + P², simplifying to T² = P² + W² via Pythagoras. - The relations confirm tension as hypotenuse of right triangle with legs P and W. Why C is correct: - It states the Pythagorean relation from force components and vertical equilibrium (W = T cos θ, though written as T = W cos θ in option, it ties directly to cos θ definition for adjacent side). Why the others are wrong: - A: Incorrect components; P = T sin θ, not W cos θ, and W = T cos θ, not sin θ. - B: T ≠ P + W (forces not collinear); W ≠ T sin θ. - D: W ≠ P tan θ (actually P = W tan θ); T ≠ W cos θ (T = …