11:11

Geometry Level 1

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.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Chew-Seong Cheong
Jan 21, 2016

Trung Le , you should mention that the answer is in degree.

At 11 : 00 11:00 the two hands are 3 0 30^\circ apart. Let the hour-hand and minute-hand move θ h \theta_h and θ m \theta_m in 11 11 minutes respectively. Then, the smaller angle between the two hands is given by:

θ = 30 θ h + θ m = 30 11 60 × 30 + 11 60 × 360 = 30 5.5 + 66 = 90.5 \begin{aligned} \theta & = 30 - \theta_h + \theta_m \\ & = 30 - \frac{11}{60} \times 30 + \frac{11}{60} \times 360 \\ & = 30 - 5.5 + 66 \\ & = \boxed{90.5} \end{aligned}

The solution is perfect!

Trung Le - 5 years, 4 months ago

( 11 60 + 1 12 11 720 ) × 36 0 = 90. 5 (\frac{11}{60} + \frac{1}{12} - \frac{11}{720}) \times 360 ^\circ = 90.5^\circ

Lu Chee Ket - 5 years, 4 months ago

Log in to reply

Why the 1÷12?

Juan Pablo Anzola Pinzón - 5 years, 4 months ago

Log in to reply

1 12 × 36 0 \frac{1}{12} \times 360^\circ stands for angle made by hour hand separately added in before being minus by how much it has traveled slightly for 11 12 × 60 × 36 0 . \frac{11}{12 \times 60} \times 360^\circ.

Lu Chee Ket - 5 years, 4 months ago

please explain u'r solution, cheong

Mohammad Tanvir Arifin - 5 years, 4 months ago

Log in to reply

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 36 0 12 = 3 0 \dfrac{360^\circ}{12} = 30^\circ . In the 11 minutes that follows, the hour-hand moves θ h \theta_h forward reducing the angle between the two hands, therefore there is a minus sign before it, that is θ h -\theta_h . During the same time, the minute-hand moving forward by θ m \theta_m increasing the angle between them, therefore, + θ m +\theta_m . Therefore, the equation: θ = 30 θ h + θ m \theta = 30 - \theta_h + \theta_m .

In 1 hour or 60 minutes the hour-hand moves 3 0 30^\circ , therefore in 11 minutes, it moves, θ h = 11 60 × 3 0 \theta_h = \dfrac{11}{60} \times 30^\circ . Similarly, in 11 minutes, the minute-hand moves θ m = 11 60 × 36 0 \theta_m = \dfrac{11}{60} \times 360^\circ .

Chew-Seong Cheong - 5 years, 4 months ago
Ratul Pan
Jan 23, 2016

There is a simple relation to find out the angle i.e.
30 H 11 2 M 30H-\frac{11}{2}M ..........[WITHOUT SIGNS]
This gives the larger angle which is 269.5
So the smaller angle is 90.5 \boxed{90.5}


0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...