What is the number of degrees in the smaller angle formed by the hour and minute hands of a clock at 5:44?
The hour hand will move at a rate of
360° in 12 hrs
30° in 1 hr
30°/ 60 = .5° in one minute
So at 5:44.....the hour hand has moved 5 (30°) + 44(.5°) = [150 + 22]° = 172° from 12 noon
The minute hand will move at a rate of 360°/ 60 = 6° per minute
So at 5:44...it will have moved [44 * 6]° = 264° from the top of the hour
So...the smaller angle formed by the hands = [264 - 172]° = 92°
What is the number of degrees in the smaller angle formed by the hour and minute hands of a clock at 5:44?
Let the angle formed by the minute hand and hour hand in degrees Δα Let the time in hours t
The formula between the two values Δα and t is:
Δα=330⋅t
Δα=330⋅t|t=5:44=5+4460=5.7¯3 h=330⋅5.7¯3=1892=1892−5⋅360=1892−1800Δα=92∘