A room is 12m long, 9m wide, and 8m high. Find the cosine of the...

JAMB 1987

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. \(\frac{8}{17}\)
C. \(\frac{8}{15}\)
D. \(\frac{12}{17}\)

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Correct Answer: Option A

Explanation

ABCD is the floor, by pythagoras

AC2 = 144 + 81 = \(\sqrt{225}\)

AC = 15cm

Height of room is 8m, diagonal of floor is 15m

∴ The cosine of the angle which a diagonal of the room makes with the floor is EC2 = 152

cosine = \(\frac{\text{adj}}{\text{hyp}}\) = \(\frac{15}{17}\)

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