At 3:40, what would the angle of the hour hand and the minute hand of a clock form?

Answer 1

At 3 pm, the hour hand is at 90 degrees from vertical. Every hour, the hour hand travels 1/12 of a complete circle (after 12 hours, the hour hand is back where it started), so every hour, the hour hand travels 1/12 of 360 degrees which is 30 degrees. So in 40 minutes, the hour hand travels an additional (40 / 60) * 30 degrees = 20 degrees. So, at 3:40, the hour hand is 90 + 20 = 110 degrees from vertical.

The minute hand travels 360 degrees in 60 minutes, so it travels 6 degrees per minute. Thus at 3:40, it has traveled 6 * 40 = 240 degrees from vertical.

Now we are interested in the angle between the hour hand, which is 110 degrees from vertical, and the minute hand, which is 240 degrees from vertical. The difference is 240 - 110 = 130 degrees, which is the final answer.