2026 GESS P2 Q10

The diagram below shows the plan view of a 2.5 m by 1.6 m rectangular fish pond \(PQRS\) that Mr Phua is planning to build in his rectangular garden \(ABCD\). The fish pond is positioned at a corner of the garden in such a way that angle \(APS=\theta^\circ\), where \(\theta\) varies.

1. Show that the length of \(AB\), \(l\) metres can be expressed in the form \(a\cos\theta+b\sin\theta\), where \(a\) and \(b\) are constants to be found.[2]
2. Express \(l\) in the form \(R\cos(\theta-\alpha)\), where \(R>0\) and \(\alpha\) is acute.[4]
3. Given that the length of \(AB\) is 2.4 m long, find the value of \(\theta\).[3]