Five O'clock occurs when the hour hand is 5/12 of 360 degrees past the vertical minute hand.
5/12 x 360 = 150 degrees
Convert that to radians for the other answer.
5 o clock?
5/12 x 360 = 150 degrees
Convert that to radians for the other answer.
The hour hand completes a full revolution (360°) or 2π radians in 12 hours.
At 5 o'clock, the hour hand is at a quarter of the way between 4 and 5. This corresponds to a time fraction of 5/12.
To calculate the angle in degrees, multiply the time fraction by 360°:
(5/12) * 360° = 150°
To calculate the angle in radians, multiply the time fraction by 2Ï€:
(5/12) * 2Ï€ = (5/6)Ï€ radians
Therefore, the hour hand makes an angle of 150° or (5/6)π radians with respect to the vertical 12 o'clock position at 5 o'clock.
The hour hand of a clock completes one full revolution (360 degrees) in 12 hours. So, the hour hand moves 360 degrees in 12 hours, which is equivalent to 30 degrees per hour.
To find the angle made by the hour hand at 5 o'clock, we need to determine the elapsed time since 12 o'clock and multiply it by the rate of motion (30 degrees per hour).
The time elapsed from 12 o'clock to 5 o'clock is 5 hours. Multiplying this by the rate of motion (30 degrees per hour), we get:
Angle = 5 hours × 30 degrees/hour
= 150 degrees
To convert this angle to radians, we can use the conversion factor: 1 radian = 180 degrees / π radians. Therefore:
Angle (in radians) = 150 degrees × (π radians / 180 degrees)
= (5Ï€) / 6 radians
So, the angle made by the hour hand at 5 o'clock is 150 degrees or (5Ï€) / 6 radians, measured clockwise from the vertical axis.