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If the angle subtended at the centre of a circle of radius 6 cm by an arc of length 2ℼ cm θ, then find θ/30. |
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Answer» We know that the length of an arc of a sector of angle θ = \(\dfrac{2\pi r \theta }{360} \) Using this formula, we get \(\dfrac{2\pi r \theta }{360} \) = 2π ⇒ 6θ/ 360 = 1 ∴ 6θ = 360 ∴ θ = 60° Hence, θ/30 = 60°/30° = 2° given : radius of circle(r) = 6 cm arc length(s) = 2π cm we know that, θ rad = s / r So, θ =( 2π / 6) rad = (π/3) rad = 60° Therefore , θ/30 = (60/30)° = 2°
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