4.
The diagram shows triangle \(P Q R\) in which \(P Q = 7\) and \(P R = 3 \sqrt { 5 }\).
Given that \(\sin ( \angle Q P R ) = \frac { 2 } { 3 }\) and that \(\angle Q P R\) is acute,
- find the exact value of \(\cos ( \angle Q P R )\) in its simplest form,
- show that \(Q R = 2 \sqrt { 6 }\),
- find \(\angle P Q R\) in degrees to 1 decimal place.