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JAMB Mathematics 2020 Paper

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Question : 8

Total: 40

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

$\frac{15}{17}$
$\frac{8}{17}$
$\frac{8}{15}$
$\frac{12}{17}$

Solution:

ABCD is the floor. By pathagoras

AC $^2$ = 144 + 81 = $\sqrt{225}$

AC = 15cm

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

Therefore, the cosine of the angle which a diagonal of the room makes with the floor is

EC $^2$ = 15 $^2$ + 8 $^2$ cosine

$\frac{\text{adj}}{\text{Hyp}} = \frac{15}{17}$

EC $^2$ = $\sqrt{225 + 64}$

EC = $\sqrt{289}$

= 17

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