Mathematics 2018 JAMB Past Questions - Question 36: 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

Correct Answer

A

Explanation

To find the cosine of the angle which a diagonal of the room makes with the floor of the room, we can use the concept of direction cosines.The diagonal of the room forms the hypotenuse of a right-angled triangle with the floor of the room. We can use the length, width, and height of the room to find the cosine of the angle.Let's denote the length, width, and height of the room as a, b, and c, respectively. In this case, a = 12m, b = 9m, and c = 8m.The diagonal, d, can be found using the formula for the diagonal of a rectangular prism:\[ d = \sqrt{a^2 + b^2 + c^2} \]\[ d = \sqrt{12^2 + 9^2 + 8^2} \]\[ d = \sqrt{144 + 81 + 64} \]\[ d = \sqrt{289} \]\[ d = 17 \]Now, we can find the cosine of the angle, θ, using the formula:\[ \cos(\theta) = \frac{c}{d} \]\[ \cos(\theta) = \frac{8}{17} \]So, the cosine of the angle which a diagonal of the room makes with the floor of the room is 8/17.