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mariarad [96]
2 years ago
8

AC= Help me please!! Thanks so much

Mathematics
1 answer:
katovenus [111]2 years ago
5 0

Answer:

AC = 6√3 in

Step-by-step explanation:

<h3>Finding the length of the chord:</h3>

Join OC. Now ΔAOC is an isosceles triangle as OA = OC =radius.

 ∠A = ∠C = 30.

 ∠A + ∠C +  ∠AOC = 180 {angle sum property of traingle}

 30 + 30 + ∠AOC  = 180°

                 ∠AOC = 180 -60

                 ∠AOC = Ф = 120°

Find the length of radius using the bellow formula.

         \sf \boxed{\bf Arc \ length = \dfrac{\theta}{180}\pi r}

            Ф = 120°

                Arc length = 4π

            \sf  4\pi =\dfrac{120}{180}*\pi *r\\\\      r =\dfrac{4\pi * 180}{120*\pi }\\\\    r = 6 \ in

\sf \boxed{\bf chord \ length = 2rSin \ \dfrac{\theta}{2}}

                         \sf b = 2*6*Sin \ \dfrac{120}{2}\\\\  b = 2 *6 * Sin \ 60^\circ\\\\  b = 2 * 6 * \dfrac{\sqrt{3}}{2}\\\\ \b = 6\sqrt{3}

\sf \boxed{\bf AC = 6\sqrt{3} \ in}

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