Answer:
Using chain of thought reasoning, the answer and explanation to the given math problem is as follows:
Step 1: Recognize that the arc's length can be calculated using the formula L = θ_arc*r, where L stands for the arc's length, θ_arc is the measure of the angle in radians, and r is the radius of the circle.
Step 2: We can calculate θ_arc by rearranging the formula to derive θ_arc = L/r. Assuming the arc's length is the same as the sector's perimeter, L = perimeter = 2πr, meaning that θ_arc = 2πr/r.
Step 3: Since the radius of the circle is 8 feet, θ_arc = 2π(8 feet/8 feet) = 2π.
Step 4: We then can calculate the angle measure of the arc bounding the sector. Calculate the area of the sector, A = θ/2πr^2. Rearranging the formula to derive θ = 2πr^2/A and inserting the given values yields θ = 2π(8^2 feet^2/6 square feet) ≈ 6.36 radians.
Answer:
The angle measure of an arc bounding a sector with area 6 square feet is 6.36 radians.