Force equilibrium in pendulum

Steps:

• Forces on bob: tension T upward along thread at angle θ to vertical, weight W downward, horizontal force F = W.
• Horizontal equilibrium: T sinθ = F = W.
• Vertical equilibrium: T cosθ = W.
• Divide equations: tanθ = (T sinθ)/(T cosθ) = W/W = 1, so θ = 45°.

Why C is correct:

• Tanθ = 1 implies θ = 45° by definition of tangent function.

Why the others are wrong:

• A: tan15° ≈ 0.27 < 1, underestimates horizontal force balance.
• B: tan30° ≈ 0.577 < 1, insufficient for F = W.
• D: tan60° ≈ 1.73 > 1, overestimates required tension angle.

Final answer: C