JAMB Mathematics 2018 Paper

Concept:A room is a cuboid. The space diagonal makes an angle with its projection on the floor, which is the floor diagonal.Explanation:The floor diagonal is found using the length and width only.$\text{Floor diagonal} = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15\text{ m}$.The diagonal of the room uses length, width, and height.$\text{Room diagonal} = \sqrt{12^2 + 9^2 + 8^2} = \sqrt{144 + 81 + 64} = \sqrt{289} = 17\text{ m}$.If $\theta$ is the angle between the room diagonal and the floor, then the adjacent side is the floor diagonal.$\cos\theta = \frac{\text{floor diagonal}}{\text{room diagonal}} = \frac{15}{17}$.Answer:$\frac{15}{17}$Option A.