Question

Express the radian measure ${\frac{4\pi }{27}}^c$ as sexagesimal measure.

Answer 1

Given: $C=\frac{4\pi }{27}$

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

$\frac{D}{90}=\frac{2\times \frac{4\pi }{27}}{\pi }$

$\frac{D}{90}=\frac{8}{27}$

$D=\frac{8}{27}\times 90$

$\therefore D=\frac{8}{3}\times 10={\frac{80}{3}}^{\circ }$