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WAEC Further Mathematics 2008 Question 40

Question 40

Statics

In the diagram below, forces P, Q and 50N are acting on a body at M. If the system is in equilibrium, calculate, in terms of θ, the magnitude of P.

Diagram for this question
  1. A.50cosθ/sin(θ + 45)°
  2. B.50cosθ/cos(θ + 45)°
  3. C.50sinθ/cos(θ + 45)°
  4. D.50sinθ/sin(θ + 45)°
Show the answer and explanation

Answer: D (50sinθ/sin(θ + 45)°)

Explanation

By Lami's theorem P/sin(angle between Q and 50N) = 50/sin(angle between P and Q). The angle between Q and the weight is 180° − θ and between P and Q is θ + 45°, so P = 50 sinθ/sin(θ + 45°).