[email protected] wrote:What is the angle between the minute and the hour hand of the clock which shows 12:24?
115
120
124
130
132
Let's say that at 12:00 the hour hand and the minute hand are both at 0º.
We need to determine the position of each hand after the passing of 24 minutes.
Hour hand:
Every 12 hours, the hour hand travels clockwise all the way around the clock (360º).
Thus, every hour, the distance traveled by the hour hand = (1/12)(360) = 30º.
In 24 minutes -- 2/5 of an hour -- the hour hand travels clockwise 2/5 of its hourly distance:
(2/5)(30) = 12º.
Minute hand:
Every hour, the minute hand travels clockwise all the way around the clock (360º).
Thus, in 24 minutes -- 2/5 of an hour -- the minute hand travels clockwise 2/5 of its hourly distance:
(2/5)(360) = 144º.
Since the minute hand travels clockwise 144º, while the hour hand travels clockwise 12º, the angle between the minute hand and the hour hand = 144-12 = 132º.
The correct answer is
E.
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