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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?

 Dec 30, 2020
 #1
avatar+94 
+1

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. :)  

=^._.^=

 Dec 30, 2020
 #2
avatar+114171 
+1

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°

 

 

cool cool cool

 Dec 30, 2020

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