Example 5 - Chapter 3 Class 11 Trigonometric Functions
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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 Converting into radians = r1 ร 65ยฐ ร ๐/(180ยฐ) = r1 ร ๐๐๐ /๐๐ Length of arc of 2nd circle ๐ = r2 ฮธ = r2 ร 110ยฐ Converting into radians = r2 ร 110ยฐ ร ๐/(180ยฐ) = r2 ร ๐๐๐ /๐๐ Given that Length of 1st arc = length of 2nd arc r1 ร ๐๐๐ /๐๐ = r2 ร ๐๐๐ /๐๐ ๐1/๐2 = 11๐/18 ร 36/13๐ ๐1/๐2 = 22๐/13๐ ๐๐/๐๐ = ๐๐/๐๐ Hence, r1 : r2 = 22 : 13 So, Ratio of Radius = 22 : 13
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo