Find the angle between hour-hand and minute-hand in a clock at i) ten past eleven ii) twenty past seven iii) t

Exercise 1.1 · Q15

Q. Find the angle between hour-hand and minute-hand in a clock at

i) ten past eleven ii) twenty past seven iii) thirty five past one iv) quarter to six v) 2:20 vi) 10:10

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Step 1: Use hour-hand rate $0.5°$ /min and minute-hand rate $6°$ /min; angle $=|30H-5.5M|°$ , adjusted to at most $180°$ .

i) Ten past eleven ( $H=11,M=10$ ): $|330-55|=275°\to360°-275°=85°$ .

ii) Twenty past seven ( $H=7,M=20$ ): $|210-110|=100°$ .

iii) Thirty five past one ( $H=1,M=35$ ): $|30-192.5|=162.5°$ .

iv) Quarter to six, i.e. $5{:}45$ ( $H=5,M=45$ ): $|150-247.5|=97.5°$ . …

Q.Find the angle between hour-hand and minute-hand in a clock at