A room is 12m long 9m wide and 8m high Find the... - JAMB Mathematics 2024 Question
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 the problem:
-
Find the diagonal of the floor:
- The floor is a rectangle with length 12m and width 9m.
- Use the Pythagorean theorem: diagonal = \(\sqrt{12^2 + 9^2}\) = \(\sqrt{144 + 81}\) = \(\sqrt{225}\) = 15m
-
Find the diagonal of the room:
- The room's diagonal forms a right-angled triangle with the floor diagonal (15m) and the height (8m).
- Use the Pythagorean theorem again: room diagonal = \(\sqrt{15^2 + 8^2}\)
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