2023 EOY Sec 2 ACSI P1 Q12

Determine whether a triangle of length \(20\) cm, \(48\) cm and \(52\) cm is a right-angled triangle.

Justify your answer.

The diagram shows a right-angled triangle \(PQR\) where angle \(PRQ = 90^{\circ}\), \(PR = 4\) cm and \(\tan^{-1} \left(\frac{1}{5} \right) = x^{\circ}\). If \(\mathrm{P , R}\) and \(\mathrm{S}\) form a straight line, angle \(QSR = y^{\circ}\) and \(RS = 5\) cm, show that \(y^{\circ} = \sin^{-1}{ \left(\frac{4}{\sqrt{17}} \right) } \).