Question

Express the radian measure ${\frac{3\pi }{5}}^c$ as sexagesimal measure.

Answer 1

Given:$C=\frac{3\pi }{5}$

We know that $\frac{D}{90}=\frac{2C}{\pi }$

$\frac{D}{90}=\frac{2\times \frac{3\pi }{5}}{\pi }$

$\frac{D}{90}=\frac{6}{5}$

$D=\frac{6}{5}\times 90=6\times 18$

$\therefore D=6\times {18}^{\circ }={108}^{\circ }$