A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

Answer Details

ABCD is the floor, by pythagoras
AC2 = 144 + 81 = $\sqrt{225}$
AC = 15cm
Height of room is 8m, diagonal of floor is 15m
∴ The cosine of the angle which a diagonal of the room makes with the floor is EC2 = 152
cosine = $\frac{\text{adj}}{\text{hyp}}$ = $\frac{15}{17}$