Clock Problem: smallest angle between hands when....

[LucilleEsmerelda]

I need help in finding the measure of the smallest angle on an analog clock with the time of 6:50. I think the answer is 100 degrees, but that's not it and I am currently stumped.

 

[tkhunny]

Are you accounting for the fact that the big hand isn't quite pointing to the 7?

It's 1/6 of an hour short.

On the other hand, since your answer is too big, maybe that isn't where you are wandering off.

Angle between each two consecutive numbers: (1/12)*360º = 30º

Angle between 7 and 10: 3*30º = 90º
Angle between 7 and 6+(5/6): (1/6)*30º = 5º

Are we close? If you show your work, we all can be benefitted. Without it, we're just guessing at what you did and at what is needed.

 

[LucilleEsmerelda]

It's hard to show the work since I drew a clock. I did account the hand was between the 6 and 7. I figured 10 degrees instead of 5. I think this has got it! Thanks!!!!!

 

[TchrWill]

Re: Clock Problem

I need help in finding the measure of the smallest angle on an analog clock with the time of 6:50. I think the answer is 100 degrees, but that's not it and I am currently stumped.

The hour hand moves at the rate of 0.5º/min. while the minute hand moves at the rate of 6º/min.

The angle between each number on the clock face is 30º.

At 6:50, the hour hand has moved .5(50) = 25º from the 6 toward the 7.

Therefore, the hour hand has moved 6(30) + 25 = 205º from the 12.

At 6:50, the minute hand has moved 6(50) = 300º from the 12.

Thus, the smallest angle between the hour and minute hands at 6:50 is 300 - 205 - = 95º.

 

[Denis]

Sign on clock repair shop: if your clock don't tick, tock to us :roll: