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
\(\frac{15}{17}\)
B
\(\frac{8}{17}\)
C
\(\frac{8}{15}\)
D
\(\frac{12}{17}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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 = \(\frac{\text{adj}}{\text{hyp}}\) = \(\frac{15}{17}\)
Source: Myschool Past Questions Archive (Record #31962)