Question

61°24` in radians

Please and thank you

Answer 1

well, we know there are 60 minutes in 1 degree, so 24' is 24/60 = 0.4°, so 61°24' is really 61.4°, now, we also know that there are 180° in π radians, so

`\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 61.4&x \end{array}\implies \cfrac{180}{61.4}~~ = ~~\cfrac{\pi }{x} \\\\\\ 180x=61.4\pi \implies x=\cfrac{61.4\pi }{180}\implies x=\cfrac{307\pi }{900}\implies x\approx 1.07~radians`