JAMB Mathematics 2021 Paper

Concept:The points $X$, $Y$, and $Z$ form a right-angled triangle. Use trigonometry to find the required angle and convert it to a bearing measured clockwise from north.Explanation:Let $Y$ be at the origin, with $X$ due east of $Y$ and $Z$ due south of $Y$.Thus, $YZ = 6.0\,\text{km}$, $ZX = 12\,\text{km}$, and $\angle Y = 90^\circ$.In $\triangle XYZ$, using the sine ratio: $\sin \theta = \frac{YZ}{ZX} = \frac{6}{12} = \frac{1}{2}$.Therefore, $\theta = 30^\circ$.Here, $\theta$ is the angle between $XY$, which points due west, and $XZ$.Due west has a bearing of $270^\circ$.Since $Z$ lies south of west, subtract $\theta$ from $270^\circ$.Bearing of $Z$ from $X = 270^\circ - 30^\circ = 240^\circ$.Answer:$240^\circ$