There are several ways to measure the size of an angle. One way is to use units of degrees. (Radian measure is another way.) In a complete circle there are three hundred and sixty degrees.
An angle could have a measurement of 35.75 degrees. That is, the size of the angle in this case would be thirty-five full degrees plus seventy-five hundredths, or three fourths, of an additional degree. Notice that here we are expressing the measurement as a decimal number. Using decimal numbers like this one can express angles to any precision - to hundredths of a degree, to thousandths of a degree, and so on.
There is another way to state the size of an angle, one that subdivides a degree using a system different than the decimal number example given above. The degree is divided into sixty parts called minutes. These minutes are further divided into sixty parts called seconds. The words minute and second used in this context have no immediate connection to how those words are usually used as amounts of time.
Symbols used
In a full circle there are 360 degrees. Each degree is split up into 60 parts, each part being 1/60 of a degree. These parts are called minutes. Each minute is split up into 60 parts, each part being 1/60 of a minute. These parts are called seconds.
There are symbols that are used when stating angles using degrees, minutes, and seconds. Those symbols are show in the following table.
Symbol for degree: º
Symbol for minute: '
Symbol for second: "
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Example
So, the angle of 40 degrees, 20 minutes, 50 seconds is usually written this way:
How could you state the above as an angle using common decimal notation? The angle would be this many degrees, (* means times.):
40 + (20 * 1/60) + (50 * 1/60 * 1/60)
That is, we have 40 full degrees, 20 minutes - each 1/60 of a degree, and 50 seconds - each 1/60 of 1/60 of a degree.
Work that out and you will get a decimal number of degrees. It's 40.34722 º
An angle could have a measurement of 35.75 degrees. That is, the size of the angle in this case would be thirty-five full degrees plus seventy-five hundredths, or three fourths, of an additional degree. Notice that here we are expressing the measurement as a decimal number. Using decimal numbers like this one can express angles to any precision - to hundredths of a degree, to thousandths of a degree, and so on.
There is another way to state the size of an angle, one that subdivides a degree using a system different than the decimal number example given above. The degree is divided into sixty parts called minutes. These minutes are further divided into sixty parts called seconds. The words minute and second used in this context have no immediate connection to how those words are usually used as amounts of time.
Symbols used
In a full circle there are 360 degrees. Each degree is split up into 60 parts, each part being 1/60 of a degree. These parts are called minutes. Each minute is split up into 60 parts, each part being 1/60 of a minute. These parts are called seconds.
There are symbols that are used when stating angles using degrees, minutes, and seconds. Those symbols are show in the following table.
Symbol for degree: º
Symbol for minute: '
Symbol for second: "
Understanding equation for square root is always challenging for me but thanks to all math help websites to help me out.
Example
So, the angle of 40 degrees, 20 minutes, 50 seconds is usually written this way:
How could you state the above as an angle using common decimal notation? The angle would be this many degrees, (* means times.):
40 + (20 * 1/60) + (50 * 1/60 * 1/60)
That is, we have 40 full degrees, 20 minutes - each 1/60 of a degree, and 50 seconds - each 1/60 of 1/60 of a degree.
Work that out and you will get a decimal number of degrees. It's 40.34722 º
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