Question on: JAMB Mathematics - 2020
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
\(\frac{12}{17}\)
Ask EduPadi AI for a detailed answer
Correct Option: A
- Draw a rectangle with edges ABCD to represent the floor.
- Draw a line from A to C, representing the diagonal of the floor
Use Pythagoras theorem to calculate the diagonal (AC):
AC\(^2\) = 144 + 81 = \(\sqrt{225}\)
AC = 15cm
Given that height(h) of room 8m, let's find the cosine of the angle which a diagonal of the room (EC) makes with the floor.
EC\(^2\) = AC\(^2\) + h\(^2\)
EC\(^2\) = 15\(^2\) + 8\(^2\)
\(\frac{adj}{Hyp} = \frac{15}{17}\)
EC\(^2\) = \(\sqrt{225 + 64}\)
EC = \(\sqrt{289}\)
EC = 17
\(Cos\theta\) = Adjacent/Hypoteneous
= 15/17
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