Question

Prove that the number of sexagesimal minutes in any angle is to the number of centesimal minutes in the same angle as 27 : 50.

Answer 1

Hint:-Before solving this question, let us know about the conversion of Degree and Minute. Given below is the method:-
Conversion – Degree into minutes: For the conversion of degree to minutes, multiply the number by 60 and use the whole number part of the answer as minutes.

Complete step-by-step answer:
In sexagesimal system, a right angle = 90 degree and one degree = 60 minutes
So, one right angle (in sexagesimal system) = \[90~\times 60\text{ }minutes\] (1)
In Centesimal system, a right angle = 100 grades and one grade = 100 minutes
So, one right angle (in centesimal system) = \[100~\times 100\text{ }minutes\] (2)
Therefore, from (1) and (2), ratio in Sexagesimal : Centesimal = \[(90~\times 60)\text{ }:(100~\times 100)\]
                                                                                                              = 5400 : 10000
                                                                                                              = 27 : 50
Hence, proved

Note:-Let us now know about Sexagesimal System and Centesimal System
Sexagesimal System : Sexagesimal is a numeral system with sixty as its base.
Centesimal System : In the centesimal system, a right angle is divided into 100 centesimal degrees; each centesimal degree, into 100 centesimal minutes; and each centesimal minute into 100 centesimal seconds. Centesimal degrees are also known as grades.