If in two circles, arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre, find the ratio of their radii.

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Precalculus

NCERT Class 11 - Math

Chapter 3

Trigonometric Functions

Section 1

Introduction

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Video Transcript

So here in this kitchen left the radio of the two circles b also one, and also to let an arc of flint al substance, an angle of 60 degrees at the center of the circle of radius also one and an arc of flan L substance. An angle of 75 degree at the center of the circle of radius R. Sub two. So now 60 degree equal to 5.3 radiant. Okay, 75 degrees equal to 55 upon 12 radiant to the relation between degree and radiant. 180 degree equal to bye radiant. Then in a circle of radius R unit if an R. Of land unit substance, an angry Tito radiant at the center. So here do you take will do al upon our and you can do then is al equal to our peter? Therefore, for by upon three radian al equal to also one time 5.3. And Allah quit our sub two times 55.12. So here you can see that al value same. So here are so one times 5.3 equal to also two times 55 upon 12. Now we simplify this and here we get oh so one upon ourselves to equal to 5.4. Those the ratio of D. Ready I is 54 so it is a final answer.

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