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 (\(\theta\)) = \(\frac{15}{17}\).
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