Hands of a Clock at Right Angle
The hands of a clock create a right angle 44 times in a day. The hands of the clock make 12 rounds throughout the 12 hours. As the hour hand is still and moves slower than the minute hands, this would mean that the minute hand makes 11 revolutions, taking the rotating coordinate system into consideration. So, the points at which right angles are created are 22 times.
Thus, in a 24-hour day, 2 X 22 = 44. Thus, there are 44 right angles created by the hands of a clock in a day. A right angle is anangle with a measurement of 90 degrees.
Steps to Calculate Number of Times Hands of a Clock Make Right Angle
A more mathematical approach to calculating the number of times the hands of a clock make right angles is provided below with proper calculations.
The hands of a clock start moving after midnight. The minute hand moves 360 degrees in 60 minutes. Thus, in a minute, the hands move at 6 degrees. Let us consider this as 6x.
Similarly, the hour hand moves 30 degrees in 60 minutes. That will mean that in a minute it will move at 0.5 degree. Let us also consider this as 0.5x.
In both cases, x is the number of minutes after midnight. The first 90 degree angle is made when the minute hand has moved 90 degrees more than the hour hand. This will give us an equation:
6x = 0.5x + 90
5.5x = 90
x = 16 minutes and 4/11 seconds
So, the first right angle is made about 16 minutes past midnight.
Now, we will check when the minute hand has moved 180 degrees ahead of the hour hand and is 90 degrees behind it. So, we get the following equation:
6x = 0.5x + 270
5.5x = 270
x = 49 1/11 (49 minutes and 1/11 seconds)
At about 11 minutes to 1 o'clock.
Now, to check every time such as situation occurs, we will calculate it as:
49 1/11 - 16 4/11 = 32 8/11 minutes
24 hours is 1440 minutes.
1440 X 11/ 360
4 X 11 = 44
Hence, every 24 hours, i.e., in a day there are 44 right angles between the hands of a clock.
How many times are the hands of a clock at right angle in a day?
There are 44 times when the hands of a clock are at a right angle in a day. This is because in 12 hours, the hands of a clock make 22 right angles. Thus, in a 24 hours, the total right angles made between the hands of a clock are 44.
- Prove that Root 2 + root 5 is Irrational
- Find the largest number that will divide 398 , 436 and 542 leaving remainders 7 , 11 and 15 respectively
- A Car Traveling at 20 Kmh Speeds Up to 60 Kmh in 6 Seconds What is Its Acceleration in Ms2
- A Pole Has to Be Erected at a Point on the Boundary of a Circular Park of Diameter 13 Metres in Such
- Factorize the Equation: x^3-3x^2-9x-5
- Write a pair of negative integers whose difference gives 8
- Check Whether 6n Can End With the Digit 0 for Any Natural Number N
- Write formula of finding selling and cost price when profit or loss percent is given.
Commentswrite a comment