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
-
\(\frac{5}{17}\)
- \(\frac{8}{17}\)
- \(\frac{8}{15}\)
- \(\frac{12}{17}\)
The correct answer is: A
Explanation
ABCD is the floor, by pythagorasAC2 = 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 = \(\frac{\text{adj}}{\text{hyp}}\) = \(\frac{15}{17}\)