The clock in the picture is rectangular in shape, but each hand moves at a constant rate, like a normal clock. The distance between the numbers 8 and 10 on the dial is 12 centimeters, and the distance between 1 and 2 is x centimeters. What is the value of x? So here it is a bit bigger. We know that this distance is 12 centimeters, so this distance right here is 6 centimeters. We also know that the clock goes between each of the two consecutive numbers in an equal amount of time. And we also know that in an equal amount of time, each clock hand goes 1 12th the way around the circle. The hour hand, let's say, goes 1 12th the way around an entire circle. So that means it moves 30 degrees in each hour. So let's just draw this out a little bit. This means that this angle right here is 30 degrees, and this angle right here is 30 degrees. So let me remove this background clock because it's not too important. We just need to remember that this length is 6. Now, we see that this angle is a right angle just because of how this thing is drawn, like this is a rectangle. So that makes this a 30-60-90 triangle, and this is also a 30-60-90 triangle. So that means once we know this side, we can figure out the other two sides. This side is going to be this side divided by root 3, so it's going to be 2 root 3. And this entire side right here is going to be this side times the root 3, so it's 6 root 3. And now x is this distance right here, so it has to be 6 root 3 minus 2 root 3, which is 4 root 3.

rectangular clock

distance calculation

30-60-90 triangle

angle intervals

geometry