Clock angle formula

Clock Angle Formula Clocks are used to tell the time of the day. The clock is provided with three hands to measure time which are an hour hand, minute hand, and second hand. A clock has atotal of12 divisions of a total measure of angle 360 o. The clock angle formula is used to calculate the time between any two hands of the clock.The clock angle formula is explained below with solved examples. What Is the Clock Angle Formula? Before learning the o.Each division is further divided into 5 equalparts and each part equals 1 minute and has an angular distance of 6 o.A list of parts and their corresponding angles are given below. Minutes Angular Value 1 minute 6 o 2 minutes 12 o 3 minutes 18 o 4 minutes 24 o 5 minutes 30 o 6 minutes 36 o 7 minutes 42 o 8 minutes 48 o 9 minutes 54 o 10 minutes 60 o Let us see the applications of the clock angle formula in the following section. Indulging in rote learning, you are likely to forget concepts. With Cuemath, you will learn visually and be surprised by the outcomes. Example on Clock Angle Formula Example 1:Find the clockwise angle between the hour hand and minute hand at 3:30 P.M.(assume the hour hand is fixed at 3for this hour). Solution To find: Angle between the hour hand and minute hand Divisions between the hour hand and minute hand at 3:30 P.M. is 3. Using the clock angle formula, The angle between any two divisions is 30 o. Therefore, the angle will be 3 × 30 o= 90 o Answer: The angle between the hour hand and minute hand at 3:3...

Activity: Clocks and Angles This activity is about What is the angle between the hands of a clock at 1 o'clock? At 1 o'clock the minute hand (red) points to the 12 and the hour hand (blue) points to the 1. So we need to find the angle between the 12 and the 1. How many of this angle are there in a complete turn? There are 12 of them in a complete turn (360°), so each one must be 360°÷ 12 = 30° So the angle between the hands of a clock at 1 o'clock is 30° . Note: • It doesn't matter whether we are talking about 1 am or 1 pm, the answer is exactly the same for both. • The angle between the hands at 1 o'clock could also be given as the reflex angle 330°, but we will always give the smaller (acute or obtuse) angle. What is the angle between the hands of a clock at 2:30? At 2:30 the minute hand (red) points to the 6 and the hour hand (blue) points halfway between the 2 and the 3. So how many lots of 30° do we have this time? • The angle between the 5 and the 6 is 30° • The angle between the 4 and the 5 is 30° • The angle between the 3 and the 4 is 30° • The remaining angle is ½× 30° = 15° So the angle between the hands of a clock at 2:30 = 30° + 30° + 30° + 15° = 105° Your Turn Complete the following table (give the smaller angle in each case): Time 1:00 2:30 7:00 10:30 11:20 3:40 5:15 8:45 Angle 30° 105° Check your answers at the bottom of the page. More Complicated Times Finding the angle between the hands of a clock is easy as long as we don't use complicated times. For exam...

Enter Time or Angle in Degrees Calculate the angle between the hands of the clock if the time is 8: 40 H = 8 M = 40 Calculate ∠ between 12 and 8There are 360° in a full circle (clock) There are 12 hours Each hour = 360/12 = 30° Hour FormulaHours = 30( H) Hours = 30( 8) θh = 240 Minute FormulaEach minute is 1/60 of an hour. Each hour represents 30 degrees. Minutes Angle = M(30)/60 → M/2: θm= M 2 θm= 40 2 θm = 20 Calculate ∠ between the clock: ΔθΔθ = |θh + θm| Δθ = |240 + 20| Δθ = |260| Hands in opposite direction:Clockwise + counter-clockwise = 360° Subtract our clockwise angle from 360° Angle 2 = 360 - 260°

Explanation: A clock is a circle, and a circle always contains 360 degrees. Since there are 60 minutes on a clock, each minute mark is 6 degrees. The minute hand on the clock will point at 15 minutes, allowing us to calculate it's position on the circle. Since there are 12 hours on the clock, each hour mark is 30 degrees. We can calculate where the hour hand will be at 8:00. However, the hour hand will actually be between the 8 and the 9, since we are looking at 8:15 rather than an absolute hour mark. 15 minutes is equal to one-fourth of an hour. Use the same equation to find the additional position of the hour hand. We are looking for the angle between the two hands of the clock. The will be equal to the difference between the two angle measures. Explanation: A analog clock is divided up into 12 sectors, based on the numbers 1–12. One sector represents 30 degrees (360/12 = 30). If the hour hand is directly on the 10, and the minute hand is on the 2, that means there are 4 sectors of 30 degrees between then, thus they are 120 degrees apart (30 * 4 = 120). Explanation: At , the hour hand is on the and the minute hand is at the . There are spaces on a clock, and these hands are separated by spaces. Thus, the angle between them is the degrees of the entire clcok, which is . Therefore, we multiply these to get our answer. We can cancel out as we multiply to get: Explanation: The entire clock measures 360°. As the clock is divided into 12 sections, the distance between each num...

$\begingroup$ I did some playing around on my calculator and found that if I make theta negative in the formula, it will give me the 2nd time the angle is formed, and according to the source of this problem, the answer would be correct, however it wouldn't be if I change the hour to 12 o'clock. $\endgroup$ Full circle is 60 minutes and $360^\circ$ so $$ 54^\circ = 54^\circ \times \frac = 9, $$ can you solve the equation? For a question of this type, "first time after $t_0$," there is a relatively straightforward procedure. Just ask and answer the following questions: • What is the angle between the hands at time $t_0$? • How much must the angle change to get to the desired angle? • How fast is the angle changing? (This one always has the same answer as long as the clock is a conventional 12-hour clock with minute and hour hands.) From the answers to questions 2 and 3, you figure out how long it takes for the hands to reach the desired configuration, and add that to $t_0$ to get the time when the configuration occurs. Just be careful that you correctly account for whether the minute hand has to catch up to the hour hand first and then get "ahead" by the given angle, or whether the minute hand can make that angle with the hour hand before catching up with it. Let's think it out. The minute hand travels $360 degrees/hour = 6 degrees/minute$. The hour hand travels $360 degrees/12 hour = 30 degrees/hour = .5 degree/minute$ So the angle between the two hands is $5.5 degrees*minu...

Clock angle problems are a type of Math problem [ ] Clock angle problems relate two different measurements: A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue clock turns 360° in 12 hours (720 minutes) or 0.5° per minute. The minute hand rotates through 360° in 60 minutes or 6° per minute. Equation for the angle of the hour hand [ ] θ hr = 0.5 ∘ × M Σ = 0.5 ∘ × ( 60 × H + M ) When are the hour and minute hands of a clock superimposed? [ ] T denotes time in hours; P, hands' positions; and θ, hands' angles in degrees. The red (thick solid) line denotes the hour hand; the blue (thin solid) lines denote the minute hand. Their intersections (red squares) are when they align. Additionally, orange circles (dash-dot line) are when hands are in opposition, and pink triangles (dashed line) are when they are perpendicular. In The hour and minute hands are superimposed only when their angle is the same. θ min = θ hr ⇒ 6 ∘ × M = 0.5 ∘ × ( 60 × H + M ) ⇒ 12 × M = 60 × H + M ⇒ 11 × M = 60 × H ⇒ M = 60 11 × H ⇒ M = 5. 45 ¯ × H H is an integer in the range 0–11. This gives times of: 0:00, 1:05. 45, 2:10. 90, 3:16. 36, 4:21. 81, 5:27. 27. 6:32. 72, 7:38. 18, 8:43. 63, 9:49. 09, 10:54. 54, and 12:00. (0. 45 minutes are exactly 27. 27 seconds.) See also [ ] • References [ ]

Home • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Formula and Basic Concepts of Clock A Clock a circle having 360 degrees . It is divided into 12 equal parts numbered from 1 to 12 .Each part is 360/12 = 30°. When the minute hand takes a complete round i.e covers 360° known as one hour. A Clock has two hands that is the hour hand and the minute hand. Both hands move around the circular dial. The hour hand is smaller than the minute hand and the hour hand is slower than the minute hand. shows time in hours and the minute hand shows time in minutes. On this page we’ll look for some of the basic Formulas for Clocks. A) Angle between hands of a clock 1. When minute hand is behind the hour hand, the angle between the two hands at M minutes past H o’clock. = 30 [H -(M/5)] + M/2 degree = 30H – (11M/2) 2. In the case where the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H ‘o clock will be calculated as = 30 (M/5-H ) -M/2 degree = 11/2M – 30H B) To calculate x minute space gain by the minute hand over the hour hand, = x \frac C) Both the two hands of the clock will...

Q. The Angle Formed By The Hour hand And Minute hand of a Clock at 2 : 15 p.m. is : (A) 27.5° (B) 22.5° (C) 45° (D) 30° Answer : 22.5° Why? Do not worry! Everything is written below from Shortcut Trick to Complete Discription of the Concept and Full Discussion here. Shortcut Formula Trick to find The Angle Formed By The Hour hand And Minute hand of a Clock : It is very easy. Just Remember the formula given below. To find the angle made by hour hand and minute hand at h : m, where h = number of hours with respect to 12:00 (example: 7:12 pm means, h = 7 but, 12 : 30 pm means , h = 0 ) m = directly enter the minute. Angle = | 11m÷2 – 30h | Note: If the result is greater than 180° , then substract the result from 360° to get the final result. Derivation of The Angle Formed By The Hour hand And Minute hand of a Clock Formula : We know, A Complete revolution of any hand of a clock = 360° Now, Angle made by Minute Hand in 1 Minute = 360°/60 = 1/2 Now, at h : m , total minutes = 60 × h + m = 60h + m (example: 2:15 means , 60×2 + 15 = 135 minutes) Angle made by hour hand in (60h + m) minute = (60h + m) × 1/2 = 30h + m/2 So, Angle between the hour hand and minute hand = 6m – (30h + m/2) = | 11m÷2 – 30h | Which is the required formula. Q. Pipes A and B can fill a tank in 8 and 24 hours respectively. Pipe C can empty it in 12 hours. If the three pipes are opened together, then the tank will be fill in (a) 18 hours (b) 6 hours (c) 12 hours (d) 24 hours Answer : CLICK HERE (SHORTCUT TR...

Clock angle formula The clock angle formula is a mathematical procedure or formula that implies revealing the angle between the needles or the hands of an analog watch or clock. The clock angle issue implicates two numerous proportions of angle and time. The angle is generally assessed in degrees clockwise from the dent of the digit 12. Times are generally founded on a 12-hour watch or clock. Clocks are utilized to demonstrate and understand a particular time in a day. A clock is always prepared with three needles or hands for assessing the time, through the hour hand, minute hand, and second hand. A clock generally has an altogether 12 divisions and a cumulative measurement gradient of 360 degrees. This illustration exhibits the angles constructed by the needles or hands of an analog timepiece exhibiting a time of 2:20. The main use of the clock angle formula is to evaluate the moment or the time between any two needles or hands of a clock. Here in this article, the formula of clock angle is vividly explained with a simple illustration. The Formula of Clock angle Before understanding the formula of clock angle, one should understand a tiny bit about the clock. A clock has altogether 12 departments. The angle which is present between any two divisions of a clock is 30 degrees. Each and every grid is halved into 5 proportional portions, each is equal to 1 point, and the angular extent is 6 degrees. A schedule of portions and their complementary angles are provided below: Mi...