# How do you find the degree measure of an angle of 3/5 radians?

Feb 27, 2017

$\frac{3}{5}$ radian is ${34.38}^{\circ}$ or ${34}^{\circ} 22 ' 48 ' '$

#### Explanation:

We know that $\pi$ radian is ${180}^{\circ}$

Hence $1$ radian is ${\left(\frac{180}{\pi}\right)}^{\circ}$

and $\frac{3}{5}$ radian is ${\left(\frac{180}{\pi}\right)}^{\circ} \times \frac{3}{5} = {\left(\frac{108}{\pi}\right)}^{\circ}$

= ${\left(\frac{108}{3.1416}\right)}^{\circ} = {34.38}^{\circ}$

As ${1}^{\circ} = 60 '$ and 1"=60'',

we have ${0.38}^{\circ} \times 60 = 22.8 ' = 22 ' 48 ' '$

Hence $\frac{3}{5}$ radian is ${34.38}^{\circ}$ or ${34}^{\circ} 22 ' 48 ' '$