What is the number of degrees in the smaller angle between the hour hand and the minute hand on a clock that reads seven o'clock?
the hour hand has moved 7/12 of the way around, right?
That is 7/12 * 360 = 210°
So, calling 12:00 = 360°, the angle is 360-210=150°
To find the number of degrees in the smaller angle between the hour hand and the minute hand on a clock that reads seven o'clock, follow these steps:
Step 1: Determine the position of the hour hand:
At seven o'clock, the hour hand will be pointing directly at the number 7 on the clock face.
Step 2: Calculate the position of the minute hand:
At seven o'clock, the minute hand will be pointing directly at the number 12 on the clock face.
Step 3: Calculate the angle between the hour hand and the minute hand:
To calculate the angle, we can use the formula:
Angle = 30 x (H - M)
Where H is the position of the hour hand and M is the position of the minute hand.
In this case, the angle between the hour hand and the minute hand is:
Angle = 30 x (7 - 12) = 30 x (-5) = -150 degrees
However, since we are looking for the smaller angle between the two hands, we need to take the absolute value of the result.
Therefore, the number of degrees in the smaller angle between the hour hand and the minute hand on a clock that reads seven o'clock is 150 degrees.
To find the number of degrees in the smaller angle between the hour hand and the minute hand on a clock that reads seven o'clock, we need to calculate the positions of the hour and minute hands relative to the 12 o'clock position.
First, let's find the position of the hour hand. In a clock, the hour hand moves 360 degrees in 12 hours. Since it's 7 o'clock, we can calculate the fraction of the hour that has passed as follows:
Fraction of the hour = (Number of minutes / Total minutes in an hour)
= (0 minutes / 60 minutes)
= 0
This means the hour hand has moved 0 degrees from the 12 o'clock position.
Next, let's find the position of the minute hand. In a clock, the minute hand moves 360 degrees in 60 minutes. Since it's 7 o'clock, the minute hand is pointing at the 12 o'clock position.
Now, we can calculate the angle between the hour and minute hands. The smaller angle is the angle between the two hands that is less than 180 degrees. If the angle is greater than 180 degrees, we subtract it from 360 degrees to get the smaller angle.
To calculate the angle, subtract the position of the hour hand from the position of the minute hand:
Angle = (Position of minute hand - Position of hour hand)
= (0 degrees - 0 degrees)
= 0 degrees
Therefore, the smaller angle between the hour hand and the minute hand on a clock that reads seven o'clock is 0 degrees.