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
\(\frac{12}{17}\)
Ask EduPadi AI for a detailed answer
Correct Option: A
First find the diagonal of the floor:
\[ d_f = \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = 15 \]
Next, find the space diagonal of the room:
\[ d = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = 17 \]
The cosine of the angle with the floor is:
\[ \cos \theta = \frac{\text{floor diagonal}}{\text{room diagonal}} = \frac{15}{17} \]
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