11:11
On a clock, what is the smaller angle in degrees formed by the hour hand and the minute hand at 11:11?
Write your answer with one decimal place.
The answer is 90.5.
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2 solutions
The solution is perfect!
( 6 0 1 1 + 1 2 1 − 7 2 0 1 1 ) × 3 6 0 ∘ = 9 0 . 5 ∘
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Why the 1÷12?
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1 2 1 × 3 6 0 ∘ stands for angle made by hour hand separately added in before being minus by how much it has traveled slightly for 1 2 × 6 0 1 1 × 3 6 0 ∘ .
please explain u'r solution, cheong
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At 11:00 the hour-hand is at the 11 mark and the minute-hand is at the 12 mark. The angle between them is 1 2 3 6 0 ∘ = 3 0 ∘ . In the 11 minutes that follows, the hour-hand moves θ h forward reducing the angle between the two hands, therefore there is a minus sign before it, that is − θ h . During the same time, the minute-hand moving forward by θ m increasing the angle between them, therefore, + θ m . Therefore, the equation: θ = 3 0 − θ h + θ m .
In 1 hour or 60 minutes the hour-hand moves 3 0 ∘ , therefore in 11 minutes, it moves, θ h = 6 0 1 1 × 3 0 ∘ . Similarly, in 11 minutes, the minute-hand moves θ m = 6 0 1 1 × 3 6 0 ∘ .
There is a simple relation to find out the angle i.e.
3
0
H
−
2
1
1
M
..........[WITHOUT SIGNS]
This gives the larger angle which is 269.5
So the smaller angle is
9
0
.
5
Trung Le , you should mention that the answer is in degree.
At 1 1 : 0 0 the two hands are 3 0 ∘ apart. Let the hour-hand and minute-hand move θ h and θ m in 1 1 minutes respectively. Then, the smaller angle between the two hands is given by:
θ = 3 0 − θ h + θ m = 3 0 − 6 0 1 1 × 3 0 + 6 0 1 1 × 3 6 0 = 3 0 − 5 . 5 + 6 6 = 9 0 . 5