find the radian measure of the angle between hour - hand and minute- hand of a clock at 1) 20 minute past 2,2) 10 minute past 11,3) 13 minute past 6 4) 5 minute past 1.
Answers
Answer:
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(1) 0.872 radian
(2) 2 radian
(3) 1.67 radian
(4) 0.043 radian
Step-by-step explanation:
The angle between the hour and the minute hand
= 120° - 10° - 60°
= 50°
= 50° × π/180°
= 0.872 radian
(2) 10 minutes past 11
At 11 o'clock , the angle between the hour and the minute hand will be 60°
In 10 minutes, the hour hand will cover the angle = 10/2 = 5°
In 10 minutes, the minute hand will cover the angle = 6°× 10 = 60°
The angle between the hour and minute hand
= 60° + 60° - 5°
= 115°
= 115° × π/180°
= 2 radian
(3) 13 minute past 6
At 6 o'clock , the angle between the hour and the minute hand will be 180°
IN 13 minutes, the angle made by the hour hand = 13/2°
IN 13 minutes, the angle made by the hour hand = 6°× 13 = 78°
The angle between the hour and minute hand
= 180° - 78° + 13/2°
= 95.5°
= 95.5° × π/180°
= 1.67 radian
(4) 5 minutes past 1
At 1 o'clock, the angle between hour and minute hand = 30°
IN 5 minutes, the angle made by the hour hand = 5/2°
IN 5 minutes, the angle made by minute hand = 6°× 5 = 30°
The angle between the hour and the minute hand
= 30° - 30° + 5/2°
= 2.5°
= 2.5° × π/180°
= 0.043 radian
Hope this answer is helpful.
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