Trigonometry - Trigonometric Modelling

A mover needs to deliver a refrigerator to a customer. The refrigerator can be modelled by a cuboid of dimensions 80 cm by 80 cm by 185 cm.

To move the refrigerator into the kitchen through a door, the mover has to tilt the refrigerator such that \(AD\) makes an acute angle \(\theta\) with the horizontal ground.

1. Show that the height, \(h\) cm, of \(C\) above ground is given by \(h=185\sin\theta+80\cos\theta\).[2]
2. Express \(h\) in the form \(R\sin(\theta+\alpha)\), where \(R>0\) and \(0^\circ<\alpha<90^\circ\).[3]
3. Find the value of \(\theta\) when \(h=180\).[3]