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Find the angle between the minute hand and the hour hand of a clock at 1) 4:30PM and 2)10:40 PM?
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Find the angle between the minute hand and the hour hand of a clock at...
Angle between the Minute Hand and Hour Hand of a Clock

Case 1: 4:30 PM

  • At 4:30 PM, the hour hand is pointing directly at the 4 and the minute hand is pointing at the 6.

  • The angle between the hour hand and the 12 o'clock mark is 4 x 30 = 120 degrees.

  • The angle between the minute hand and the 12 o'clock mark is 6 x 30 = 180 degrees.

  • Since the minute hand is ahead of the hour hand, we need to find the difference between the two angles.

  • The angle between the minute hand and the hour hand is 180 - 120 = 60 degrees.



Case 2: 10:40 PM

  • At 10:40 PM, the hour hand is pointing between the 10 and the 11 and the minute hand is pointing at the 8.

  • The angle between the hour hand and the 12 o'clock mark is 10 x 30 + 40 / 2 = 310 degrees.

  • The angle between the minute hand and the 12 o'clock mark is 8 x 30 = 240 degrees.

  • Since the hour hand is slightly past the 10 and the minute hand is before the 12, we need to add 360 degrees to the angle of the hour hand.

  • The angle between the minute hand and the hour hand is 240 - (310 + 360) = -430 degrees.

  • Since we want a positive angle, we add 360 degrees to get the final answer.

  • The angle between the minute hand and the hour hand is 360 - 430 = 70 degrees.



Conclusion: The angle between the minute hand and the hour hand of a clock at 4:30 PM is 60 degrees and at 10:40 PM is 70 degrees.
Community Answer
Find the angle between the minute hand and the hour hand of a clock at...
Formula:|5.5*min-30*h| ,1)45,2)80
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Clockwork refers to the inner workings of mechanical clock or watch (where it is known as “movement”) and different types of toys which work using a series of gears driven by a spring. Clockwork device is completely mechanical and its essential parts are:• A key (or crown) which you wind to add energy• A spiral spring in which the energy is stored• A set of gears through which the spring's energy is released. The gears control how quickly (or slowly) a clockwork machine can do things. Such as in mechanical clock / watch the mechanism is the set of hands that sweep around the dial to tell the time. In a clockwork car toy, the gears drive the wheels.Winding the clockwork with the key means tightening a sturdy metal spring, called the mainspring. It is the process of storing potential energy. Clockwork springs are usually twists of thick steel, so tightening them (forcing the spring to occupy a much smaller spac e) is actually quite hard work. With each turn of the key, fingers do work and potential energy is stored in the spring. The amount of energy stored depends on the size and tension of the spring. Harder a spring is to turn and longer it is wound, the more energy it stores.While the spring uncoils, the potential energy is converted into kinetic energy through gears, cams, cranks and shafts which allow wheels to move faster or slower. In an ancient clock, gears transform the speed of a rotating shaft so that it drives the second hand at one speed, the minute hand at 1/60 that speed, and the hour hand at 1/3600 that speed. Clockwork toy cars often use gears to make themselves race along at surprising speed.What is the meaning of “movement” of old age mechanical clocks?

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Find the angle between the minute hand and the hour hand of a clock at 1) 4:30PM and 2)10:40 PM?
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