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BECE Mathematics 2024 Paper

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Question : 31

Total: 40

In the diagram,

\angle QPR = 30^{\circ}

|QR| = 5\,\text{cm}

\sin 30^{\circ} = \frac{1}{2}

Find the length of

\overline{PQ}

$2.5\,\text{cm}$
$5.0\,\text{cm}$
$12.0\,\text{cm}$
$10.0\,\text{cm}$

Solution:

Concept:

Use the sine ratio from SOHCAHTOA:

\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}}

.

Explanation:

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:

D.

10.0\,\text{cm}

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