Q) Between 12 noon and 1 PM, there are two instants when the hour hand and the
minute hand of a clock are at right angles. The difference in minutes between
these two instants is what?
I am unable to find that certain angle that'll give me the difference in minutes, I have tried drawing figures and finding the angles but it seems like it can vary and still add up to the same conditions as mentioned…
Best Answer
The easy way:
You don't actually need to find the two times when the hour and minute hand are at right angles. Just note that the difference between these two times is how long it takes for the minute hand to move $180^\circ$ farther than the hour hand has moved. The minute hand moves at $6^\circ$ per minute, and the hour hand moves at $\frac{360}{12\cdot 60}^\circ=\frac{1}{2}^\circ$ per minute. So the time required for the minute hand to advance $180^\circ$ farther than the hour hand is $\frac{180}{6-1/2}=\frac{360}{11}$ minutes.