# CIE A level Math -Mechanics :Topic : 4.1 Forces and equilibrium identify the forces: Exam Style Questions Paper 4

### Question

Forces of magnitudes 13 N and 14 N act at a point O in the directions shown in the diagram. The resultant of these forces has magnitude 15 N. Find
(i) the value of θ,
(ii) the component of the resultant in the direction of the force of magnitude 14 N.

(i) X = 14 – 13cosθ and Y = 13sinθ or triangle with sides 13, 14, 15 and θ opposite 15 [$$14^{2}+ 13^{2}$$– 2 × 13 × 14cosθ = $$15^{2}]$$