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# Find the degree measures of the angle subtended at the centre of a circle of radius 100cm by an arc of length 22cm (use $\pi=\large\frac{22}{7})$

$\begin{array}{1 1}(A)\;12^{\large\circ}&(B)\;12^{\large\circ}36'\\(C)\;13^{\large\circ}&(D)\;14^{\large\circ}36'\end{array}$

Can you answer this question?

Toolbox:
• $\theta=\large\frac{l}{r}$
• $\theta$=angle subtended by arc
• $l$=length of the arc
• $r$=radius of the circle
• 1 radian=$(\large\frac{180}{\pi})$
Given :$l=22$cm,r=100cm
$\theta=\large\frac{l}{r}$
$\Rightarrow \large\frac{22}{100}$
$\theta=0.22$radians
We know that
1 radian=$(\large\frac{180}{\pi})$
0.22 radian=$0.22\times \large\frac{180^{\large\circ}}{\pi}$
$\Rightarrow 0.22\times \large\frac{180^{\large\circ}}{22/7}$
$\Rightarrow \large\frac{0.22\times 180\times 7}{22}$
$\Rightarrow \large\frac{126}{10}$$=12^{\large\circ}36'$
Thus the degree measures of the angle subtended at the centre of the circle is $12^{\large\circ}36'$
Hence (B) is the correct answer.
answered Apr 16, 2014