A rectangular picture of width \(\quantity{32}{cm}\) and height \(\quantity{20}{cm}\) has its lower edge \(AB\) horizontal against a vertical wall. It hangs at an angle of \(15^\circ\) to the wall and may be taken to be of negligible thickness. It is supported by two equal strings \(FD\), \(FC\) of length \(\quantity{20}{cm}\) attached to the upper corners \(C\), \(D\) of the picture and to a point \(F\) on the wall vertically above the centre of \(AB\).
Copy the given sketch, including the projections of \(C\), \(D\) and \(E\), the mid-point of \(CD\), onto the wall at \(X\), \(Y\) and \(Z\) respectively.
Identify in terms of the letters the following angles and calculate them:
- the angle between the two strings,
- the angle between the string \(DF\) and the wall,
- the angle between the wall and the plane containing both strings.
