Component of resultant in given direction

Given two or more forces, find the component of the resultant in a specified direction (often perpendicular or parallel to one force).

1 questions · Moderate -0.3

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CAIE M1 2007 June Q2
5 marks Moderate -0.3
2 \includegraphics[max width=\textwidth, alt={}, center]{f7a22c07-44e3-4891-be60-cbab772f45df-2_549_589_934_778} Two forces, each of magnitude 8 N , act at a point in the directions \(O A\) and \(O B\). The angle between the forces is \(\theta ^ { \circ }\) (see diagram). The resultant of the two forces has component 9 N in the direction \(O A\). Find
  1. the value of \(\theta\),
  2. the magnitude of the resultant of the two forces.