# Find out an angle

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

### Find out an angle

Help needed to solve this puzzle

Find out the angle between hour hand and minute hand in a clock at 5:35?

Thanks
burgess

Posts: 45
Joined: Wed Jun 25, 2014 8:24 am
Reputation: 11

### Re: Find out an angle

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.
Guest

### Re: Find out an angle

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

### Re: Find out an angle

Thanks help by all experts here.

jackwilson

Posts: 29
Joined: Wed May 21, 2014 1:24 am
Reputation: 2

### Re: Find out an angle

Thank you all for your valuable replies..

burgess

Posts: 45
Joined: Wed Jun 25, 2014 8:24 am
Reputation: 11

### Re: Find out an angle

It will be 43-degree angle between hour hand and minute hand.

leesajohnson

Posts: 208
Joined: Thu Dec 31, 2015 7:11 am
Location: London
Reputation: -33

### Re: Find out an angle

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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