Neco 2022 Further Mathematics Question 12

A uniform horizontal beam \(AB\) of length \(8\ \text{m}\) is hinged at \(A\) to a wall. The beam is supported by two cables: cable \(AC\) is attached to the beam at point \(C\) located \(3\ \text{m}\) from \(A\) and makes an unknown angle \(\theta\) above the beam; cable \(AB\) is attached at the far end \(B\) and makes an angle of \(45^{\circ}\) with the horizontal. The beam itself weighs \(300\ \text{N}\) acting at its centre, and a load of \(1200\ \text{N}\) hangs \(5\ \text{m}\) from \(A\). If the tension in cable \(AC\) is twice the tension in cable \(AB\), find (i) the tension in each cable (to the nearest newton) and (ii) the horizontal and vertical components of the reaction at the hinge \(A\).