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At 2:48 what is the degree measure of the smaller angle formed by the hour and minute hands of a 12-hour clock?

 May 2, 2020
 #1
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Let  the top  of the clock  = 0°

Every minute the minute hand  moves 6°  [in 60 min it moves 360°]

And every minute the hour hand moves   (1/2)°   [in 60 min it moves 30°...1/12 of a complete rotation ]

 

So in 48 minutes the minute hand has moved  48*6  = 288° from the top of the clock

And in the same time the  hour hand has moved 48 * (1/2)  = 24°  from the top of the clock

 

So.....the larger angle formed by the hands = 288 - 24  = 264°

 

So....the smaller angle  formed  = 360  - 264   = 96°

 

 

cool cool cool

 May 2, 2020
 #2
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have mercy

.

Guest May 2, 2020
 #3
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H=2; M=48; A=abs((30*H) - (5.5*M));print"A =", A,"Degrees")
A = 204 Degrees - This is the larger angle.
So: 360 - 204 =156 degrees - this is the smaller angle.


At 2:48 the hour hand is exactly at 14 minutes after 12. The minute hand at 48 minutes before 12 is =60 - 48 =12 minutes to 12.
So:12 minutes + 14 minutes =26 minutes
26 x 6 degrees each = 156 degrees.

 May 2, 2020

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