+370 What is the number of degrees in the smaller angle formed by the hour and minute hands of a clock at $4{:}15?$
+1938 The hour hand will move at a rate of
\(360° \space \text{in} \space 12 \space \text{hours} \\ 30° \space \text{in} \space 1 \space \text{hour} \\ 30°/ 60 = 0.5° \space \text{in} \text{ one minute}\)
So at 4:15, the hour hand has moved \(4 (30°) + 15(.5°) = [120+ 7.5]° = 127.5°\)from 12 o'clock
The minute hand will move at a rate of \(360°/ 60 = 6°\) per minute
So at 4:15 it will have moved \([15* 6]° = 90°\) from the top of the hour
So...the smaller angle formed by the hands\( = 127.5 - 90 = 37.5^\circ\)
May have made an error....
Thanks! :)
