JAMB Mathematics 2020 Paper

Concept:The diagonal of the room and its projection on the floor form a right triangle.The projection is the floor diagonal, and the height is the vertical side.Explanation:First, find the diagonal of the floor:$d = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15$This floor diagonal is the adjacent side to the angle with the floor.The room is $8$ m high, so the space diagonal $D$ is:$D = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17$The cosine of the angle with the floor is:$\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15}{17}$Answer:$\frac{15}{17}$ (Option A).