Question

Express ${45}^{\circ }{20}^{\prime }{10}^{\prime \prime }$ in radian measure$(\pi =3.1415)$.

Answer 1

${10}^{\prime \prime }=\frac{10}{60}min={\left(\frac{10}{60\times 60}\right)}^{\circ }={\left(\frac{1}{360}\right)}^{\circ }$
${20}^{\prime }={\left(\frac{20}{60}\right)}^{\circ }={\left(\frac{1}{3}\right)}^{\circ }$
$\therefore$ ${45}^{\circ }{20}^{\prime }{10}^{\prime \prime }={(45+\frac{1}{360}+\frac{1}{3})}^{\circ }=\frac{16200+1+120}{360}=\frac{16321}{360}$
Now ${\left(\frac{16321}{360}\right)}^{\circ }=\frac{16321}{360}\times \frac{\pi }{180}rad=\frac{16321}{360}\times \frac{3.1416}{180}=\frac{51274.054}{64800}=0.79$rad
Ans: 0.79