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Q.
If two circular arcs of the same length subtend angles of $60^{\circ}$ and $80^{\circ}$ at their respective centres, then the ratio of their radii is
Trigonometric Functions
Solution:
Given that, $S _{1}= S _{2}$
If the radii are $r_{1}$ and $r_{2}$, then
$
\begin{array}{l}
r_{1} \times \theta_{1}=r_{2} \times \theta_{2} \\
\Rightarrow r_{1}\left(\frac{60 \pi}{180}\right)=r_{2}\left(\frac{80 \pi}{180}\right) \ldots .[\because s = r \theta] \\
\Rightarrow \frac{r_{1}}{r_{2}}=\frac{80}{60}=\frac{4}{3}
\end{array}
$