Find the angle between the two hands of a clock at 15 minutes past 4 o'clock.
35.5°
309
37.50
32.50
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Answer:
32.50................
The angle between the two hands of a clock at 15 minutes past 4 o'clock is 37.5°
Therefore, option (3) is correct.
Step-by-step explanation:
The hour hand covers one circle in 12 hours
Thus in 12 hours the angle made by hour hand on the centre = 360°
In 1 hour (=60 min), the angle made by hour hand on the centre = 360°/12
In 1 minute, the angle made by hour hand on the centre = 360°/(12 × 60)
= 0.5°
Similarly,
The angle made by minute hand in 1 minute = 360°/60 = 6°
In 15 minutes, the angle made by minute hand 15 × 6° = 90°
When the minute hand makes 90° angle, at the centre the hour hand makes an angle
= 15 × 0.5° = 7.5°
At 4 o'clock, the angle between the hands is 120°
At 15 minutes past 4 o'clock, the angle between the hands is
= 120° - 90°+7.5°
= 30° + 7.5°
= 37.5°
Hope this answer is helpful.
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