Question

starting at 3 o'clock at what time will the minute hand catch up with the hour hand? Give your exact answer in hours; minutes; seconds. this problem could be answered using algebra, but it needs to be solved using TRIG

Answer 1

3:45

Answer 2

I am curious about how to do this with trigonometry.
But with algebra, we have the minute hand starts pointing straight up, moving at a rate of 6 degrees/minute. The hour hand is 90 degrees ahead of the minute hand, moving at 0.5 degrees/minute.
so they catch up at time t when their difference is zero:
6t -(t/2 +90)= 0
this gives us 16 minutes, 21.1818.... seconds
or
the minute hand catches the hour hand at 3:16:21 (rounded to the nearest second)