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beks73 [17]
3 years ago
5

A) 3 in b) 4 in c) 5 in d) 6 in PLEASE HELP

Mathematics
1 answer:
Andrei [34K]3 years ago
8 0

Answer:

I would say A

Step-by-step explanation:

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The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines

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The vertex angle is 120°, so the other two angles have measure θ such that

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since the interior angles of any triangle sum to 180°. Solve for θ :

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1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²

and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:

3072π cm² - 2304√3 cm² ≈ 5660.3 cm²

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