Clockwise Angle

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Originally Discovered by Leonardo Sembiring
Melialamath Applications. Copyright 2009.
See also : Indonesia Version

Smart solution : To find the angle between hour and minute hands in a clock face.
Comment : SIMPLY SOLUTION

The angle between hour hand and minute hand is :
clock-formula1
where h = hour count and m = minutes count.

Example :
A clock face comprises of hour and minute hands. Clockwise motion of hour and minute hands will reach an exactly position where minute hand lies over the hour hand at 3 pass x minutes. Find x?

Solution :
Minute hand lies over the hour hand causes the angle is zero degree.
30o.3 – (11/2)o.m = 0o
90o – (11/2)o.m = 0o
m = 90/(11/2) = 16 4/11 minutes.


Indonesia Version

Sudut yang dibentuk oleh jarum panjang dan jarum pendek adalah:
clock-formula1
dimana h = jumlah jam and m = jumlah menit.

Contoh :
Pada pukul 3 lewat x menit, jarum panjang (penunjuk menit) dan jarum pendek (penunjuk jam) akan berimpit. Berapa x?

Penyelesaian :
Apabila jarum panjang dan jarum pendek berimpit, maka sudut yang dibentuk kedua jarum adalah nol derajat.
30o.3 – (11/2)o.m = 0o
90o – (11/2)o.m = 0o
m = 90/(11/2) = 16 4/11 menit.

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