A room is 12m long, 9m wide and 8m high. Find the cosine of the angle...

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

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.

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