SOLUTION: what time after 4 o'clock will the hands of the contionously drive clock from a right angle?

Algebra ->  Trigonometry-basics -> SOLUTION: what time after 4 o'clock will the hands of the contionously drive clock from a right angle?      Log On


   



Question 631371: what time after 4 o'clock will the hands of the contionously drive clock from a right angle?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
At exactly 4 o'clock, the big hand is on the 12
and the little hand is on the 4. They span 20
minutes out of 60, or 120 degrees out of 360 degrees
------------------
The minute hand will move at the rate of 360 degrees / hr
The hour hand will move at the rate of +5%2F60%29%2A360+=+30+
degrees / hr
------------------
I want the difference between them to be 90 degrees with
the difference starting out at 120 degrees
Let +a+ = the angle between the hands
Let +t+ = the time in hours for the angle between them
to equal 90 degrees
-------------------
+a+=+%28+120+%2B+30t+%29+-+%28+360t+%29+
+90+=+%28+120+%2B+30t+%29+-+%28+360t+%29+
+90+=+120+-+330t+
+330t+=+120+-+90+
+330t+=+30+
+t+=+1%2F11+ hrs
+1%2F11%2A60+=+5+%2B+5%2F11+ minutes
+5%2F11%2A60+=+27.27+
---------------
The hands will be 90 degrees apart at
4:05 and 27 sec
check:
+a+=+%28+120+%2B+30t+%29+-+%28+360t+%29+
+a+=+%28+120+%2B+30%2A%281%2F11%29+%29+-+%28+360%2A%281%2F11%29+%29+
+a+=+%28+120+%2B+2.7272+%29+-++%28+32.7272+%29+
+a+=+120+-+30+
+a+=+90+
OK