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WAEC Mathematics 2025 Paper

Question : 43

Total: 50

Solution:

Concept:

In a right-angled triangle, trigonometric ratios relate the sides to the acute angles.

Explanation:

\triangle PQR

\angle PRQ = 90^\circ

, so

\triangle PQR

is right-angled at

R

PQ

is the hypotenuse because it is opposite the right angle.

\angle QPR = 30^\circ

, and the side

y

is opposite this angle.

Using the sine ratio:

\sin 30^\circ = \frac{\text{opposite side}}{\text{hypotenuse}} = \frac{y}{PQ}

Substitute

PQ = 10 \, \text{cm}

\sin 30^\circ = \frac{y}{10}

Since

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

\frac{1}{2} = \frac{y}{10}

Multiply both sides by

10

y = 10 \times \frac{1}{2} = 5 \, \text{cm}

Answer:

y = 5 \, \text{cm}

Correct option: C. 5cm

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