Find out an angle

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

Find out an angle

Postby 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?

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burgess
 
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Re: Find out an angle

Postby 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 210-167.5 = 42.5 degrees.
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Re: Find out an angle

Postby 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
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Re: Find out an angle

Postby jackwilson » Thu Aug 14, 2014 11:34 pm

Thanks help by all experts here.

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Re: Find out an angle

Postby burgess » Thu Aug 21, 2014 6:44 am

Thank you all for your valuable replies..

burgess
 
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Re: Find out an angle

Postby leesajohnson » Tue May 31, 2016 6:28 am

It will be 43-degree angle between hour hand and minute hand.
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Re: Find out an angle

Postby 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.
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