Force equilibrium in horizontal and vertical directions

Steps:

• Resolve forces vertically: tension's vertical component balances weight, so T cos θ = W.
• Resolve forces horizontally: tension's horizontal component balances P, so T sin θ = P.
• Divide horizontal by vertical equation: (T sin θ)/(T cos θ) = P/W, so P = W tan θ.
• Substitute T from vertical: T = W / cos θ, confirming both relations in C.

Why C is correct:

• Newton's first law requires net force zero; vertical equilibrium gives T cos θ = W directly from component resolution.

Why the others are wrong:

• A: Swaps components; P equals T sin θ, not W cos θ, and T exceeds W.
• B: Ignores angles; T ≠ P + W as forces are not collinear.
• D: Incomplete and lacks P = W tan θ relation.

Final answer: C