Calculation without calculator..HELP!!?

Answer: 115 degrees

(for this, I'm assuming the hour hand moves smoothly rather than "jumping" to the next spot once an hour)

Common wrong answers (based on the assumption above): 55 degrees, 90 degrees (this answer would probably only be correct if the problem directly stated that the hour hand only moves whenever the minute hand passes the 12), 245 degrees (this technically isn't WRONG, but isn't the best answer since we usually look for the small angle between two lines)

Explanation:

To solve this, we need to:

1) Know where the minute hand and hour hand are on the clock

2) Get their locations in degree form

3) Find the angle between them

At 1, the hour hand would be on the 1 and the minute hand would be on the 12. We know that the minute hand will be on the 10 (for 50 minutes) at 1:50.

The trick with this problem is that as the minute hand moves, the hour hand does also, but much more slowly (at 1/60th the rate to be exact).

Here's how to logically find out how far the hour hand moves:

In one hour, or 60 minutes, the hour hand would move from the 1 to the 2

However, at 1:50, it has only been 50 minutes, or 5/6ths of an hour.

So the hour hand will be at the 1 5/6 place (or the 11/6 place) when the minute hand is at the 10.

To convert to degree form:

Since the 12 numbers on the clock are evenly spaced, and there are 360 degrees in total in a circle, each number will be:

360/12 degrees, or 30 degrees

So:

Minute hand: On the 10:

10 * 30 = 300 degrees

Hour hand: On the 11/6:

11/6 * 30 = 55 degrees

The angle between them going clockwise would be the difference between these numbers:

300 - 55 = 245 degrees

So, technically this is an angle between them, but I'm guessing you need the smaller angle between them. This would be:

360 - 245 = 115 degrees

Explanation for why the common WRONG answers are WRONG:

If someone got 55 degrees, this means they probably stopped at finding the degree location of the hour hand and didn't finish the problem

If someone got 90 degrees, this means they probably didn't take into account the fact that the hour hand moves while the minute hand is moving to the 50

If someone got 245 degrees, this means that they gave the big angle between them rather than finding the small angle between them

I hope I was able to help, it's probably confusing with almost everyone giving a different answer

===simple hour hand===

assuming that the hour hand is exactly at 1, then it is at 5 past and the minute hand is at 10 to. so between them there are:

10 + 5

= 15 minutes

in this case 60 minutes is 360° (full circle), so 15 minutes is:

15 * (360/60)

= 15 * 6

= 10*6 + 5*6

= 60 + 30

= 90°

===sliding hour hand===

if the hour hand is not exactly at 1 because it moves gradually. then it is *almost* at 5 past and the minute hand is at 10 to. so the time between them is:

10 + 5*(50/60)

= 10 + 5*(5/6)

= 10 + 25/6

= 10 + 4 + 1/6

= 14 + 1/6 minutes

again 60 minutes is 360°, so 14 + 1/6 minutes is:

(14 + 1/6) * (360/60)

= (14 + 1/6) * 6

= 60 + 24 + 6/6

= 60 + 24 + 1

= 85°

The clock face is round therefore the hand goes one round is 360 degree. In the other words, one number marking is 360/12= 30. Alternatively, one round is 60 minutes and therefore 1 minute is 360/60=6 degree. Your 1hr on the right suppose to give U 30 degrees and your 50min on the left give u 60degrees. When U add the two angle from right and left together, it should be 90 degrees but at this time your hour hand is no more pointing at #1 on the dot. However, U can use this matter to work out your exact angle form by your hour hand with your minutes hand.

A clock face is usually shows hours and minutes - 12 hours and 60 minutes.

1/12 x 360 degrees = 30 degrees

50/60 = 5/6 of one minute or .83.

.83/12 x 360 = 25 degrees.

Ans.: 30 + 25 = 55 degrees.

okay so a clock has 12 number on it each at 30 degrees from the other so that is that means that the minute hand is at the 10 and the hour hand is 3 numbers after so 30(3) 90 degrees in between assuming it is the smaller if not it is 270 degrees

ok....

the hour hand is between 1 and 2.

and it's 10 min to 2:00

the whole circle forms an angle 360 deg at its centre.

there are 12 partition , 1,2,3,4,...,12

hence the angle between two consecutive numbers forms at centre will be,

360/12=30 deg

hence the angle will be,

30+30+30+30-(30/6)=115 deg

Divide 360 to 12=30°

so for every hour you have 30° angle...

lets go 1st to minute hand, it is in 50min or 10th or 300°, so from 10th to 12th or 360° you will have a 60° difference, so you have now a 60° angle...

every 5mins=30°

(50min/5min)*30°=300°

360°-300°=60°

then lets go now to hour hand, it passed 1st but not yet in 2nd hour, so you have another 30° additional since it passed 1st hour.

every hr=30°

.

to calculate the reamaining angle you will use now the 50min or 10th or 300°...

just use ratio/proportion

.

300°/360°=x/30°

30°*300°/360°=x

25°=x

.

then add:

60° plus 30° plus 25°=115° answer (@_@)

set an analog clock to 1:50 and use a protractor. That's all I can do for you!