In triangle $PQR$ the angles satisfy $\angle P =30^{\circ}$, $\angle Q =2\theta$ and $\angle R =\theta$. The side opposite $\angle P$ (i.e. side $p$) is $7$ cm.

(i) Determine the value of $\theta$ (in degrees).
(ii) Find the length of side $r$ opposite $\angle R$, correct to two decimal places.
(iii) Compute the area of $\triangle PQR$ in square centimetres, correct to two decimal places.

Question

In triangle $PQR$ the angles satisfy $\angle P =30^{\circ}$, $\angle Q =2\theta$ and $\angle R =\theta$. The side opposite $\angle P$ (i.e. side $p$) is $7$ cm.

(i) Determine the value of $\theta$ (in degrees).
(ii) Find the length of side $r$ opposite $\angle R$, correct to two decimal places.
(iii) Compute the area of $\triangle PQR$ in square centimetres, correct to two decimal places.

Accepted Answer

θ = 50°, r ≈ 10.72 cm, area ≈ 36.96 cm²

Waec Model Questions Vol2 2025 Mathematics Question 12

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