JAMB Mathematics 2023 Paper

Concept:The bearing of a point is the angle measured clockwise from the north direction.Use trigonometry to find the angle in the right-angled triangle formed by the boat's path.Explanation:The boat sails 8 km north from $P$ to $Q$, so $PQ = 8$ km.Then it sails 6 km west from $Q$ to $R$, so $QR = 6$ km.Triangle $PQR$ is right-angled at $Q$.Let $\theta$ be the acute angle between the north line and the line $PR$.Using tangent:$$\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{QR}{PQ} = \frac{6}{8}$$$$\tan \theta = 0.75$$$$\theta = \tan^{-1}(0.75) \approx 36.87^{\circ}$$Since $R$ is west of north, the bearing is measured clockwise from north.$$\text{Bearing of } R \text{ from } P = 360^{\circ} - 36.87^{\circ}$$$$\text{Bearing} \approx 323.13^{\circ}$$To the nearest degree, the bearing is $323^{\circ}$.Answer:B. $323^{\circ}$