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

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.

\(\frac{9}{17}\)

C.

\(\frac{8}{15}\)

D.

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

Correct answer is A

Given length of the room = 12m; breadth = 9m and height = 8m.

The room is a cuboid in shape, therefore the length of the diagonal = \(\sqrt{l^2 + b^2 + h^2}\)

= \(\sqrt{12^2 + 9^2 + 8^2}\)

=\(\sqrt{289}\)

= 17m.

The diagonal makes an angle with the diagonal of the floor: \(\sqrt{12^2 + 9^2}\)

= \(\sqrt{225}\)

= 15m

The cosine of the angle that the diagonal makes with the floor (\(\theta\)) = \(\frac{15}{17}\).