Hello, I hope you have a good day, can you please help me it would mean a lot........ What is the smaller angle formed by the minute and hour hands at 3:30pm?

Question

asked Sep 25, 2022 31.1k views

2 Answers

Tulio Casagrande · Answer 1 · 2022-09-30T12:18:44+0000

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Step-by-step explanation:

At 3:00 pm, the hour hand is pointed directly at the '3'. At 4:00 pm, the hour hand moves to point directly at the '4'.

Since 3:30 pm is the halfway point of 3:00 pm and 4:00 pm, this must mean the hour hand is halfway between the '3' and '4'.

Each little tiny tickmark on the clock represents 1 minute. From the "3" to "4", we have 5 tickmarks, so half of that is 5/2 = 2.5

The hour hand is pointing to 2.5 minutes after the 15 minute mark, meaning the hour hand is pointing to the 15+2.5 = 17.5 minute mark.

The span of time from 17.5 minutes to 30 minutes is 30-17.5 = 12.5 minutes.

Divide this over 60 minutes and we get 12.5/60 = 125/600 = 5/24

The 5/24 indicates the fractional amount of 360 degrees being taken up by this angle shown.

So, (5/24)*360 = 75 degrees is the angle measure in this diagram.