Question

Convert the angle 3pi/5 radians to degrees

Answer 1

well, we know that π is 180°, so then what is 3π/5?

`\begin{array}{ccll} radians&degrees\\ \cline{1-2} \pi &180\\ (3\pi )/(5)&x \end{array}\implies \cfrac{\pi }{~~ (3\pi )/(5)~~}~~ = ~~\cfrac{180}{x}\implies \cfrac{5\pi }{3\pi }=\cfrac{180}{x} \\\\\\ \cfrac{5}{3}=\cfrac{180}{x}\implies 5x=540\implies x=\cfrac{540}{5}\implies x=108`