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Home » $ k = 1 $: $ 230^\circ $ - Abu Waleed Tea

$ k = 1 $: $ 230^\circ $ - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 r = \frac{6 \pm 2\sqrt{141}}{6} = \frac{3 \pm \sqrt{141}}{3}

📌 Since radius must be positive and greater than 2, we take the positive root:

📌 r = \frac{3 + \sqrt{141}}{3}

📌 Check if this is greater than 2:

📌 \(\sqrt{141} \approx 11.87\), so \( r \approx (3 + 11.87)/3 = 14.87/3 \approx 4.96 > 2 \), valid.

📌 Thus, the original radius is \(\boxed{\frac{3 + \sqrt{141}}{3}}\).

📌 A wind turbine blade is designed as a sector of a circle with radius 15 meters and central angle \(120^\circ\). Find the perimeter of the blade, including the two straight edges and the curved arc.

📌 The perimeter of the blade includes two radii and the arc length. The arc subtends \(120^\circ\), which is \(\frac{120}{360} = \frac{1}{3}\) of a full circle.

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