In Problems 79-86, A denotes the area of the sector of a...

In Problems $79-86,$ A denotes the area of the sector of a circle of radius r formed by the central angle $\theta .$ Find the missing quantity. Round answers to three decimal places.
$$\theta=\frac{1}{3} \text { radian, } A=2 \text { square feet, } r=?$$

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Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to solve for an unknown variable. In the context of the sector area formula, it enables one to isolate and solve for the circle's radius when the area and central angle are known.

Circular Sector

A circular sector is the portion of a circle enclosed by two radii and the corresponding arc. It is a fundamental concept in circular geometry, where understanding the properties of sectors helps in solving problems related to parts of a circle.

Area of a Sector Formula

The area of a sector can be calculated using the formula A = 1/2 * r^2 * ?, where r is the radius of the circle and ? is the central angle in radians. This formula is essential for finding the area covered by a sector, given the circle’s radius and the angle of the sector.

Radians

Radians are a unit of angular measure based on the radius of a circle. Using radians in formulas such as the sector area formula simplifies the relationship between the angle and the arc length, making calculations in circular geometry more straightforward.

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