0606 P11 - Jun 2023 - Q5 - 8 marks
7657
This question is to be answered without using a calculator.
(a) In triangle \(ABC\), \(AB=5\sqrt3-6\), \(BC=5\sqrt3+6\) and angle \(ABC=120^\circ\). Find \(AC\) in the form \(a\sqrt b\), where \(a\) and \(b\) are integers.
(b) In triangle \(PQR\), \(PQ=3+2\sqrt5\), angle \(PQR=30^\circ\) and the area of triangle \(PQR\) is \(\frac14(2+5\sqrt5)\). Find \(QR\) in the form \(c+d\sqrt5\), where \(c\) and \(d\) are integers.
