Question

Convert $ {150^g} $ into sexagesimal measure.

Answer 1

Hint: n sexagesimal measure, an angle is measured in degrees, minutes and seconds. In centesimal measure, an angle is measured into grades, minutes and seconds. 90 degrees make a right angle in sexagesimal whereas 100 grades make a right angle in centesimal. 1 grade=90/100 degrees. Use this formula to solve the question.

Complete step-by-step answer:
We are given to find the sexagesimal value of $ {150^g} $ i.e. 150 grades.
In the sexagesimal system of measurement, Angles are measured in degrees. One degree further divides into 60 minutes and one minute further divides into 60 seconds.
To make a right angle, we require 90 degrees in the sexagesimal system.
In the centesimal system of measurement, Angles are measured in grades. One grade further divides into 100 minutes and one minute further divides into 100 seconds.
To make a right angle, we require 100 grades in the sexagesimal system.
Therefore,
 $
  90{\text{ }}degrees = {\text{ }}100{\text{ }}grades \\
  1grade = \dfrac{{90}}{{100}}degrees \\
  {1^g} = {\dfrac{{90}}{{100}}^ \circ } \\
  $ s
Given $ {150^g} $ we have to convert it into degrees.
 $
  {1^g} = {\dfrac{{90}}{{100}}^ \circ } \\
  {150^g} = ? \\
   = 150 \times {\dfrac{{90}}{{100}}^ \circ } \\
   = {\left( {\dfrac{{150 \times 90}}{{100}}} \right)^ \circ } \\
   = {\dfrac{{13500}}{{100}}^ \circ } \\
   = {135^ \circ } \\
  $
Therefore, 150 grades in the centesimal system are equal to 135 degrees in the sexagesimal system.

Note: Centesimal system is better to use than sexagesimal system in measuring angles.1 degree is equal to 10/9 grades. To change degrees into grades, add on one-ninth to the given value; to change grades into degrees, subtract one-tenth from the given value.