What does an apostrophe means when working with angles?

Question

5° 40' is an angle of a triangle. What does the ' apostrophe means?

Ok. But i am working with sine and cosine and I am supposed to find the length of a side using that angle.

Answer 1

it means a "minute", where each minute is worth 1/60 of a degree. Each minute can be further divided into 60 smaller units called seconds, and marked with a ".

As in 5° 40' 17"

Babylonians (before the Greeks, two thousand years ago) used a system based on 60. Before calculators, this was practical because 60 is one of those magical numbers that can be divided by a whole bunch of other numbers. 60 is divible by 2, 3, 4, 5, 6, 12, 15, 20, 30.

Babylonians had also noted that dividing the circle in 360 degrees (rather than 365, the real number of days in the year) was also very practical (same reason).

When astronomy became a mathematical science, astronomers (who wrote in latin) divided the degree in 60 small parts, and called each one a
"pars minuta prima" (the first small part); each one of these could be divided again in 60 even smaller parts called "pars minuta secunda (the second small part).

From the first, we have kept the word minute, with emphasis on the first syllable: MIN-it (the word is also used as an adjective, meaning 'very small' as in "my piece of cake is minute compared to by brother's gigantic piece" -- emphasis on the syllable NU: miNUte).

From the second divisions, we have kept the word "second".

At one point, when 16th century astronomers went crazy with calculations, some even went to the fifth level of division by 60.

Today, we do not go beyond seconds. If we need more precision, we go to decimal fractions of seconds (or even decimal fractions of degrees), as in
five degrees, 40 minutes and 17.3 seconds:
5° 40' 17.3" = 5.6714722...°

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In most calculators, if you want the sine of an angle, you must enter the angle in degrees.
5° 40' = 5 + (40/60) = 5.66666... degrees
Sin(5.66666...) = 0.0987408...

In some spreadsheets (like Excel), you must provide the angle in "radians". One radian is the angle that gives you, on a circle's circumference, a curved length equal to one radius.

Since the circumference (360 degrees) = 2*pi*r, then 1 radian = 360 / (2*pi) = approx. 57.29577951 degrees.

So, in Excel, you'd have to ask for
SIN(5.66666/57.29577951)

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Once you have the appropriate trig function, you can find the sides in a triangle.

Answer 2

Working With Angles

Answer 3

It means minutes. A minute is 1/60 of a degree. You might
have an angle of 5degrees 40' 10" . The 10" means 10 seconds. A second is 1/60 of a minute. This is a very small angle. Suppose you have a sine bar on a perfectly flat surface in your machine shop and you want to lift one end of it to form a 1 second angle with your inspection plate:

x/10 = sin(1 second angle) = sin(1/3600) = .000005

solving for x, x = .00005 inches or "fifty millionths" as they say.!

Answer 4

5 degrees, 40 minutes.
The apostrophe stands for minutes. If it was a bit more exact, it'd have seconds, which are followed by ".

Example: 10°35'45". Ten degrees, 35 minutes and 45 seconds.

Cheers.

Answer 5

maybe you should pay attention in class you little ****