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Find the degree measures corresponding to the following radian measures :-$\large\frac{11}{16}$

$\begin{array}{1 1}(A)\;39^{\large\circ}22'30''&(B)\;39^{\large\circ}\\(C)\;39^{\large\circ}28'&(D)\;40^{\large\circ}\end{array} $

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  • $\pi$ radians =$180^{\large\circ}$
  • 1 radian=$(\large\frac{180}{\pi})$
  • $1^{\large\circ}=60'$
  • $1'=60''$
We have
$\pi$ radians =$\large\frac{22}{7}$ radian=$180^{\large\circ}$
$\large\frac{11}{16}$ radian =$\large\frac{180}{22}$$\times 7\times \large\frac{11}{16}$ degree
$\Rightarrow \large\frac{315}{8}$ degree
$\Rightarrow 39\large\frac{3}{8}$ degree
We have $\large\frac{3^{\large\circ}}{8}=\frac{3}{8}$$\times 60'$
$\Rightarrow \large\frac{45'}{2}$$=22'30''$
$39\large\frac{3}{8}$ degree=$39^{\large\circ}22'30''$
Hence (A) is the correct answer.
answered Apr 16, 2014 by sreemathi.v

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