Question 234954: At 12:22 a clock's hour hand is how many degrees away from a vertical position?
a) 10° b) 11° c) 12° d) 21° e) 22° Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! First, we'll figure out where the hour hand is pointing. As a full hour passes, from 12 o;clock to 1 o'clock, the hour hand moves from the 12 to the 1 (i.e. "5 minutes" on the clock). In 22 minutes the hour hand will move: "minutes" on the clock.
Since 11/6 is almost 2, the hour hand will be pointing at almost the 2 minute mark on the clock.
What angle is the hour hand at if it is pointing at 11/6 minutes? Well a whole circle is 360 degrees and a whole hour is 60 minutes. So we can set up a proportion to solve the problem.
Let x = the angle of the hour hand. Then
Now we just solve this. There are many ways. One way would be be multiply both sides by 60. This eliminates the fraction-within-a-fraction on the left:
Now we can multiply both sides by 6 giving:
So the answer is 11 degrees (b)
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