JAMB Mathematics 2019 Paper

Concept:The bearing is the clockwise angle measured from north to the line joining $X$ and $Y$.Explanation:Put point $O$ at the origin of the grid.Since $X$ is $20$ km north of $O$, and $Y$ is $9$ km east of $O$, then from $X$, the point $Y$ lies $20$ km south and $9$ km east.Draw a vertical line downward from $X$ to meet the east-west line through $Y$ at point $Z$.Then $XZ = 20$ km, $ZY = 9$ km, and $\angle XZY = 90^\circ$.Let $\theta$ be the angle between $XZ$, which points due south, and the line $XY$.In the right-angled triangle $XZY$:$$\tan\theta = \frac{ZY}{XZ} = \frac{9}{20} = 0.45$$$$\theta = \tan^{-1}(0.45) = 24.23^\circ$$The bearing of the due south direction is $180^\circ$.Since $Y$ is east of $Z$, the bearing of $Y$ from $X$ is:$$180^\circ - 24.23^\circ = 155.77^\circ$$Correct to the nearest degree, the bearing is $156^\circ$.Answer:D. $156^\circ$