Question on: JAMB Mathematics - 2024
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
\(\frac{12}{17}\)
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Correct Option: A
Here's how to solve this problem:
-
Find the diagonal of the floor:
- The floor is a rectangle with length 12m and width 9m.
- Use the Pythagorean theorem: diagonal = (\sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15) m
-
Find the diagonal of the room:
- Consider a right-angled triangle formed by the height of the room (8m), the floor diagonal (15m), and the room diagonal (the hypotenuse).
- Use the Pythagorean theorem: room diagonal = (\sqrt{8^2 + 15^
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