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: Option A
Explanation
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
There is an explanation video available below.