A) 5: 4
B) 5; 3
C) 5: 8
D) 4 : 7
Correct Answer: A
Solution :
\[60{}^\circ ={{\left( 60\times \frac{\pi }{180} \right)}^{c}}={{\left( \frac{\pi }{3} \right)}^{c}}\] and \[75{}^\circ ={{\left( 75\times \frac{\pi }{180} \right)}^{c}}={{\left( \frac{5\pi }{12} \right)}^{c}}\] \[\therefore \frac{\pi }{3}=\frac{s}{{{r}_{1}}}\] and \[\frac{5\pi }{12}=\frac{s}{{{r}_{2}}}\] \[\left[ \because \theta ={{\left( \frac{s}{r} \right)}^{c}} \right]\] \[\Rightarrow \frac{\pi }{3}{{r}_{1}}=s\] and \[\frac{5\pi }{12}{{r}_{2}}=s\] \[\Rightarrow \frac{\pi }{3}{{r}_{1}}=\frac{5\pi }{12}{{r}_{2}}\] \[\Rightarrow 4{{r}_{1}}=5{{r}_{2}}\Rightarrow {{r}_{1}}:{{r}_{2}}=5:4\]
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