Given length of the room = 12m; breadth = 9m and height = 8m.
The room is a cuboid in shape, therefore the length of the diagonal = √l2+b2+h2
= √122+92+82
=√289
= 17m.
The diagonal makes an angle with the diagonal of the floor: √122+92
= √225
= 15m
The cosine of the angle that the diagonal makes with the floor (θ) = 1517.
