Clock Hands Form Into a Straight Line
Question: How many times in 12 hours the hands of a clock extend to a straight line, similar to Fig. 1? Answer: 11 times.
The formula for finding the clock angle θ is
where H is the hour part of the time, M is the time past the hour, in minutes, such that 0 minutes ≤ M < 60 minutes.
The measure of the angle between the minute and hour hands is 180° if the hands are extended into a straight line. Solving for M using the equation above, we have
Plugging in 8 to H (since the time is between 8 and 9 o’clock) in the equation, we obtain
The times when the minute and hour hands extend into a straight line are shown below.
Please read full article from Clock Hands Form Into a Straight Line
Question: How many times in 12 hours the hands of a clock extend to a straight line, similar to Fig. 1? Answer: 11 times.
The formula for finding the clock angle θ is
where H is the hour part of the time, M is the time past the hour, in minutes, such that 0 minutes ≤ M < 60 minutes.
The measure of the angle between the minute and hour hands is 180° if the hands are extended into a straight line. Solving for M using the equation above, we have
Plugging in 8 to H (since the time is between 8 and 9 o’clock) in the equation, we obtain
