Answer:
4418.6 square feet
Step-by-step explanation:
The area of a sector of a circle is given by the formula ...
A = 1/2r²θ . . . . where r is the radius, and θ is the central angle in radians
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The area of the proposed pizza slice is the area of a sector with a radius of 66 ft and a central angle of 37°. That area will be ...
A = 1/2(66 ft)²(37°×π/180°) ≈ 4418.6 ft²
The pizza slice would cover 4,418.6 square feet.
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Additional comment
There are 2π radians in the 360° of a circle. That means ...
1 radian = 180°/π ≈ 57.296°
1° = π/180 radians
As we have done above, the number of radians can be found by multiplying the degree measure by π/180°. The units of degrees will cancel, leaving a "pure number" with no units. That is, "radians" is a non-unit: a number of radians is a pure number.
