Determain the angle size between the min arm and the hour arm. 18:45
Answers
Question :--- Determine the angle size between the min arm and the hour arm. 18:45 ..?
Concept :--
☛ The dial of the clock is circular in shape and was divided into 60 equal minute spaces..
☛ 60-minute spaces trace an angle of 3600. Therefore, 1minute space traverses an angle of 60..
☛ In 1 hour, Minute hand traverses 60-minute space or 3600 , Hour hand traverses 5-minute space or 300..
☛ The hands of the clock are perpendicular in 15-minute spaces apart....
☛ The hands of the clock are in straight line and opposite to each other in 30-minute spaces apart.
☛ The hands of the clock are in straight line when they coincide or opposite to each other.
☛ The hands of the clock are perpendicular to each other for 22 times in 12 hours and for 44 times in a day.
☛ The hands of the clock are opposite to each other for 11 times in 12 hours and 22 times in a day.
☛ The minute hand gain 55 minutes over hour hand per hour.
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Solution :----
we have to Find angle between min. arm and hour arm at 18:45 that is 6:45 .
⟿ At 6 o’ clock, the hour hand is at = 6*30 = 180° from the vertical.
⟿ In 45 minutes, Hour hand = 180° + 45*(0.5) = 180° + 22.5° = 202.5° {The hour hand moves at 0.5 dpm}.
⟿ Minute hand = 45*(6) = 270° {The minute hand moves at 6 dpm}
⟿ So, Difference or angle between the hands = 270° – 202.5° = 67.5°