Determine whether a triangle of length $20$ cm, $48$ cm and $52$ cm is a right-angled triangle

Question

Determine whether a triangle of length $20$ cm, $48$ cm and $52$ cm is a right-angled triangle. Justify your answer. [2] 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) } $. [4]

Accepted Answer

(a) Yes: $20^2+48^2=52^2$. (b) $y^\circ=\sin^{-1}(4/\sqrt{17})$.

2023 EOY Sec 2 ACSI P1 Q12

2023 EOY Sec 2 ACSI P1 Q12

Solution:

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