if m1 and m2 be the numberof sexagesimal and centasimal minute of any angle, prove that m1/27=m2/50.
if m1 and m2 be the numberof sexagesimal and centasimal minute of any angle, prove that m1/27=m2/50.
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To prove that m1/27 = m2/50, where m1 and m2 represent the count of sexagesimal and centesimal minutes of any angle, we will use the conversion formulas between sexagesimal and centesimal systems.
In the sexagesimal system, an angle is divided into 60 minutes (m1), and each minute is further divided into 60 seconds. Therefore, there are 3600 (=60*60) seconds in one degree.
In the centesimal system, an angle is divided into 100 centesimal minutes (m2), and each centesimal minute is divided into 100 centesimal seconds. Thus, there are 10,000 (=100*100) centesimal seconds in one grad.
To establish a relationship between m1 and m2, we need to convert both values to a common unit. Let's convert m1 to centesimal minutes, and vice versa.
Conversion formula from sexagesimal minutes to centesimal minutes (m1 to m2):
m2 = (m1 * 100) / 60
Conversion formula from centesimal minutes to sexagesimal minutes (m2 to m1):
m1 = (m2 * 60) / 100
Now, let's use the conversion formulas to prove m1/27 = m2/50:
First, write the conversion formula from m1 to m2:
m2 = (m1 * 100) / 60
Divide both sides of the equation by 50:
m2/50 = [(m1 * 100) / 60] / 50
Simplify:
m2/50 = (m1 * 100) / (60 * 50)
Now, let's write the conversion formula from m2 to m1:
m1 = (m2 * 60) / 100
Divide both sides of the equation by 27:
m1/27 = [(m2 * 60) / 100] / 27
Simplify:
m1/27 = (m2 * 60) / (100 * 27)
We have obtained m1/27 and m2/50 on each side of the equations. Now, let's equate them:
m1/27 = m2/50
Therefore, through the conversion formulas and subsequent simplifications, we have proved that m1/27 is equal to m2/50.