Question

express sexagesimal measure 72 degrees as grade measure​

Answer 1

Given:D =72

We know that D/90 = (2C)/π

=D /90 = 2C/ π

= 72 /90 = 2c/ π

=4 5 = 2C/ π

=C= 4π /10 = 2π/ 5 radians

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Answer 2

Concept:

• The most common system of measurement is the Sexagesimal system, which divides a straight angle into 90 equal portions called Degrees. Each degree is divided into 60 equal minutes, and each minute is divided into 60 equal seconds.
• The grad, or grade, is a unit of angle measurement defined as one-tenth of the right angle; in other words, 90 degrees has 100 gradians. It corresponds to 1400 of a turn, 910 of a degree, or 200 of a radian.

Given:

72° = D

To Find:

72° as a grade measure

Solution:

D = 72

We know,  

$\frac{D}{90} = \frac{2C}{\pi } \\= \frac{72}{90} = \frac{2C}{\pi } \\=\frac{4}{5} = \frac{2C}{\pi } \\C= \frac{4\pi }{10} \\C= \frac{2\pi }{5}$

∴C= $\frac{2\pi }{5} radians$