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The smaller angle made by the hour and the minute hands is noted when it was 1:30 PM. In which of the following intervals of time will the smaller angle between these hands again be the same?
Explanation
The angle between the hour and minute hands is calculated using the formula: θ = |30h - 5.5m|, where h is the hour and m is the minutes.
At 1:30 PM:
h = 1, m = 30
θ = |30(1) - 5.5(30)| = |30 - 165| = 135°.
Since 135° ≤ 180°, the smaller angle is 135°.
To find when the smaller angle is 135° again before 2:00 PM, we look for the point where the hands are on opposite sides and the reflex angle is 360° - 135° = 225°.
Using the formula: |30(1) - 5.5m| = 225
5.5m - 30 = 225
5.5m = 255
m = 255 ÷ 5.5 ≈ 46.36 minutes.
This corresponds to approximately 1:46:22 PM. Therefore, the time falls in the interval 1:46 PM and 1:47 PM.
SIMILAR QUESTIONS
The angle between the hour hand and the minute hand of a clock at 10 minutes past 3 is
At 8: 30 am, the angle between the minute and hour hands is
The time in the wall-clock is 3.25 the acute angle between the hours-hand and the minutes-hand is
In a clock, what is the time between 4:00:00 PM and 5:00:00 PM, when both the hour hand and the minute hand come together ?
How many times in a day are the hour hand and the minute hand of a wall clock straight (i.e., the angle between them is 180°) ?