Question

What is the angle between minute hand and hour hand at 8.40?

Answer 1

Answer:

20 degrees my good sir

Answer 2

Let's see where the minute hand is at, first, since it doesn't depend on anything else (in some watches, it depends on the seconds' hand, but no such information is given).

The minute hand should be at an angle (40/60) * 360* = 240* from 12, measured clockwise.

The hour hand now.

The hour hand denotes the current hour properly - even the decimal part.

So, the current hour, with decimals is: 8 + 40/60 = 8 + 2/3 = 26/3 hours.

Now, the angle the hour-arm makes should be: $\frac{\frac{26}{3}}{12} * 360^o$ = 260*

So... The hour arm makes 260*, the minute arm makes 240*.

That makes the angle between them = 260* - 240* = 20*.

Note: * denotes degrees.