BECE Mathematics 2024 Paper

Concept:Use the sine ratio from SOHCAHTOA: $\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}$.Solution:In $\triangle PQR$, the side opposite $\angle QPR = 30^{\circ}$ is $QR = 5\,\text{cm}$.The hypotenuse is $\overline{PQ}$.So, $\sin 30^{\circ} = \frac{QR}{PQ} = \frac{5\,\text{cm}}{PQ}$.Given $\sin 30^{\circ} = \frac{1}{2}$, we write $\frac{1}{2} = \frac{5\,\text{cm}}{PQ}$.Cross-multiply: $1 \times PQ = 2 \times 5\,\text{cm}$.Therefore, $PQ = 10\,\text{cm}$.Answer:Option D ($10.0\,\text{cm}$)