JAMB Mathematics 2011 Paper

Concept:Bearing is measured clockwise from the North direction. The path from $X$ to $Z$ forms a right-angled isosceles triangle.Explanation:Let $X$ be the starting point.The man walks $100\,\mathrm{m}$ due West to $Y$, then $100\,\mathrm{m}$ due North to $Z$.Therefore, from $Z$, point $X$ is $100\,\mathrm{m}$ to the East and $100\,\mathrm{m}$ to the South.Let $\theta$ be the acute angle between $ZX$ and the South line at $Z$.In the right-angled triangle, $\tan \theta = \frac{100}{100} = 1$.So, $\theta = \tan^{-1}(1) = 45^\circ$.This direction is $45^\circ$ East of South.Measured clockwise from North, the bearing is $180^\circ - 45^\circ = 135^\circ$.Answer:The correct bearing of $X$ from $Z$ is $135^\circ$, which is Option B.