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

Guest May 2, 2020

#1**+1 **

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°

CPhill May 2, 2020

#3**0 **

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.

Guest May 2, 2020