Ex 3.1, 6 - Chapter 3 Class 11 Trigonometric Functions

Transcript

Ex 3.1, 6 If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii. We know that 𝑙 = r θ Let the radius of the two circles be r1 and r2 Length of arc of 1st Circle 𝑙 = r1 θ = r1 × 60° Converting into radians = r1 × 60° × 𝜋/(180°) = r1 × 𝝅/𝟑 Length of arc of 2nd circle 𝑙 = r2 θ = r2 × 75° Converting into radians = r2 × 75° × 𝜋/(180°) = r2 × 𝟓𝝅/𝟏𝟐 Given that Length of 1st arc = length of 2nd arc r1 × 𝝅/𝟑 = r2 × 𝟓𝝅/𝟏𝟐 𝑟1/𝑟2 = 5𝜋/12 × 3/𝜋 𝒓𝟏/𝒓𝟐 = 𝟓/𝟒 Hence, r1 : r2 = 22 : 13 So, Ratio of Radius = 5 : 4