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Trigonometry equalities, inequalities and expressions  sin, cos, tan, cot
by burgess » Wed Jul 23, 2014 7:02 am
Help needed to solve this puzzle
Find out the angle between hour hand and minute hand in a clock at 5:35?
Thanks

burgess

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by Guest » Wed Jul 23, 2014 11:52 am
Take 12 oclock as zero degrees 12 hour clockface
Each hour is 30 degrees. Each minute moves hour hand 0.5 degrees
5 oclock is 5 x 30 = 150
5.35 is 150 + 17.5 = 167.5 for the hour hand
The minute hand is at 7 x 30 = 210 degrees
Angle between them is 210167.5 = 42.5 degrees.

Guest

by Guest » Wed Jul 23, 2014 2:27 pm
The minute hand moves at 12 times faster than the hour hand.
Let x be degrees after 5 that the hour hand moves when Minute hand moves from 12 to 7 for 35 minutes.
12x = 210
x = 17.5 degrees past 5
From 7  5 = 2....hours on face = 2 x 30 = 60 degrees
Angle between hands =(60  17.5) = 42.5 degrees

Guest

by jackwilson » Thu Aug 14, 2014 11:34 pm
Thanks help by all experts here.

jackwilson

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by burgess » Thu Aug 21, 2014 6:44 am
Thank you all for your valuable replies..

burgess

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by leesajohnson » Tue May 31, 2016 6:28 am
It will be 43degree angle between hour hand and minute hand.

leesajohnson

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by Guest » Tue May 31, 2016 7:23 pm
Hi leesajohnson.......I would love to know how you do sums..??.....you don't show any working....just an answer....and not always correct.
I hope the following gives adequate detail as to the working out of this problem and provides an easily understood solution.
Take 12 o'clock (the top of the face) as zero degrees.
There are 360 degrees in a circle.
There are 60 minutes in an hour. The minute hand moves 360 degrees (one revolution) every hour, so each minute is 6 degrees and 35 minutes past the hour equals 6 x 35 = 210 degrees past the 12 o'clock position.
For the hour hand, there are 12 hours in each 360 degree revolution of the clock face, so each hour corresponds to 360 / 12 = 30 degrees and at 5 o'clock the hour hand is at 5 x 30 = 150 degrees.
At 5:35 the hour hand is at 35 / 60 x 30 = 17.5 degrees past the 5 o'clock position. So at 5:35 the hour hand is 150 + 17.5 = 167.5 degrees past the 12 o'clock position.
So the angle between the hands at 5:35 is 210  167.5 = 42.5 degrees.

Guest

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