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Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
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If the arcs of the same length in two circles subtend angles of $60^{\large\circ}$ and $75^{\large\circ}$ at their respective centres,find the ratio of their radii

$\begin{array}{1 1}(A)\;2 : 3&(B)\;3 : 2\\(C)\;4 : 5&(D)\;5 : 4\end{array} $

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1 Answer

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Toolbox:
  • Radian measure =$\large\frac{\pi}{180}$$\times $Degree measure
  • $l=r\theta$
Let $r_1$ and $r_2$ be the radii of the two circles,then
$\theta_1=60^{\large\circ}$
$\Rightarrow (60\times \large\frac{\pi}{180})^c=(\frac{\pi}{3})^c$
$\theta_2=75^{\large\circ}$
$\Rightarrow (75\times \large\frac{\pi}{180})^c=(\frac{5\pi}{12})^c$
Let the length of each arc be 'l' cm,then
$l=r_1\theta_1=r_2\theta_2$
$\Rightarrow (r_1\times \large\frac{\pi}{3})$$=(r_2\times \large\frac{5\pi}{12})$
$\Rightarrow \large\frac{r_1}{r_2}=\frac{5\pi}{12}\times \frac{3}{\pi}$
$\Rightarrow \large\frac{r_1}{r_2}=\frac{5}{4}$
Hence $r_1 : r_2=5 : 4$
Hence (D) is the correct answer.
answered May 21, 2014 by sreemathi.v
 

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