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.

\(\frac{12}{17}\)

Correct answer is A

ABCD is the floor. By pathagoras 

AC\(^2\) = 144 + 81 = \(\sqrt{225}\) 

AC = 15cm

Height of room 8m, diagonal of floor is 15m

Therefore, the cosine of the angle which a diagonal of the room makes with the floor is 

EC\(^2\) = 15\(^2\) + 8\(^2\) cosine

\(\frac{adj}{Hyp} = \frac{15}{17}\) 

EC\(^2\) = \(\sqrt{225 + 64}\)

EC = \(\sqrt{289}\)

= 17