Question 234954
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:
{{{(22/60)*5 = 22/12 = 11/6}}} "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.<br>
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
{{{(11/6)/60 = x/360}}}
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:
{{{11/6 = x/6}}}
Now we can multiply both sides by 6 giving:
{{{11 = x}}}
So the answer is 11 degrees (b)