What is the degree measure of the smaller angle between the hour hand and the minute hand of a clock at exactly 2:50 p.m. on a 12-hour analog clock?
+2401 Hello Guest!
The important thing to remember when doing clock problems is that the hour hand moves while the minute hand moves.
At 2:50, our hour hand will be 5/6 the distance from 2-3, and the minute hand will be at 10.
Between each number is a 5 minute interval, so between the 3 and 10, the difference is 35 minutes, (10-3)*5.
However, since the hour hand will be 5/6 the distance from 2-3, we add 1/6 of the 5 minutes.
35+1/6*5 = 35 5/6.
So the difference between the minute and hour hand is 35 5/6 minutes, and a clock has 60 minutes.
Since the clock is 360 degrees, each minute is worth 6 degrees (360/60).
Thus, our angle is (35+5/6)*6 = 215 degrees.
However, because we want the smaller angle, we do 360 - 215 = 145.
145 is the final answer.
I hope this helped. :)
=^._.^=
+128407 Thanks, catmg.....here's another approach.....
Every minute the minute hand moves 360/60 = 6°
Every minute the hour hand moves 30°/60 = (1/2)°
Let "12" on the clock face be = 0°
At 2PM......the hour hand is at 120)*(1/2) = 60° and the minute hand is at 0°
In 50 minutes after that....the hour hand has moved (1/2) * (50) = 25°
And the minute hand has moved 50 * 6 = 300°
So.....the greater angle betwen these is 300 - ( 60+ 25) = 215°
And the lesser angle is 360 - 215 = 145°
