JAMB - Mathematics (2018 - No. 27)
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.
\(\frac{15}{17}\)
\(\frac{9}{17}\)
\(\frac{8}{15}\)
\(\frac{12}{17}\)
설명
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 (\(\theta\)) = \(\frac{15}{17}\).