Given length of the room = 12m; breadth = 9m and height = 8m. The room is a cuboid in shape, therefore the length of the diagonal = \(\sqrt{l^2 + b^2 + h^2}\) = \(\sqrt{12^2 + 9^2 + 8^2}\) =\(\sqrt{289}\) = 17m. The diagonal makes an angle with the diagonal of the floor: \(\sqrt{12^2 + 9^2}\) = \(\sqrt{225}\) = 15m The cosine of the angle that the diagonal makes with the floor (\(\theta\)) = \(\frac{15}{17}\).