Question

What is the exact angle between the clock hands at 6:45:00 PM? Plz show work

Answer 1

90°

Explanation:

angle on a straight line=180 and half of 180=90°

Answer 2

67.5°

Explanation:

You know the long hand would be at number 9 and you also know that from the number 6 to 9 it would be 90°. Between each number, there are also 5 smaller marks on the clock. Thus, for 90°, there would be 5×3=15 smaller marks. (I used 3 because between 6 and 9 there are 3 big numbers)

Now here's the trickier part: There are 60 minutes within 5 small marks. We can find out at which mark does the shorter hand move to at 45 minutes.

`(45)/(60)`×5 = 3.75

Out of the 15 smaller marks of 90°, the 45th minute stands at 3.75. The angle of 3.75 would then be between the 15th mark and the 3.75th mark. The gap would be 15-3.75 = 11.25 marks.

`(11.25)/(15)` ×90° = 67.5°

You can refer to the picture for better visualisation of the clock. Hope this helps.