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  1. Chapter 3 Class 11 Trigonometric Functions
  2. Serial order wise


Example 5 If the arcs of the same lengths in two circles subtend angles 65ยฐ and 110ยฐ at the center, find the ratio of their radii. We know that ๐‘™ = r ฮธ Let the radius of the two circles be r1 and r2 Length of arc of 1st Circle ๐‘™ = r1 ฮธ = r1 ร— 65ยฐ = r1 ร— 65ยฐ ร— ๐œ‹/(180ยฐ) = r1 ร— 13๐œ‹/36 Length of arc of 2nd circle ๐‘™ = r2 ฮธ = r2 ร— 110ยฐ = r2 ร— 110ยฐ ร— ๐œ‹/(180ยฐ) = r2 ร— 11๐œ‹/18 Given that Length of I arc = length of II arc r1 ร— 13๐œ‹/36 = r2 ร— 11๐œ‹/18 ๐‘Ÿ1/๐‘Ÿ2 = 11๐œ‹/18 ร— 36/13๐œ‹ ๐‘Ÿ1/๐‘Ÿ2 = 22๐œ‹/13๐œ‹ ๐‘Ÿ1/๐‘Ÿ2 = 22/13 Hence r1 : r2 = 22 : 13 So, Ratio of Radius = 22 : 13

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