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A garden has the shape of a circular sector such that its straight sides measure 50 feet in length and the central angle is 132°. if the garden needs to be surrounded by fencing, how many feet are needed to enclose the garden?

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215 ft

Step-by-step explanation:

The length of the surrounding fence is equal to the perimeter of the garden. That is the sum of the lengths of the straight sides and the curved arc. The arc length is given by the formula ...

s = r·θ . . . . . where θ is the central angle in radians

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arc length

There are π radians in 180°, so the arc will have a measure in radians of ...

θ = 132° × (π/180°) = 11/15π ≈ 2.3038 . . . . radians

Then the length of the curved side of the garden is ...

s = (50 ft)(2.3038 radian) ≈ 115.2 ft

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perimeter

The fence length is the sum of the arc length and the two radii:

perimeter = 115.2 ft + 2×50 ft = 215.2 ft

About 215 feet of fencing are needed to enclose the garden.
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