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Answer :
Final answer:
To find the radius of the circle, we can use the formulas for the sector area and the circumference of a circle.
Explanation:
To find the radius of a circle whose sector area is 59 square inches and whose arc measures 40o, we can use the formulas for the area of a sector and the circumference of a circle.
The formula for the area of a sector is A = (θ/360) × π × r², where A is the area, θ is the central angle, π is approximately 3.14, and r is the radius. Given that the sector area is 59 square inches and the arc measures 40 degrees, we can substitute these values into the formula.
59 = (40/360) × 3.14 × r²
Dividing both sides by (40/360) × 3.14, we get:
r² = 59 / ((40/360) × 3.14)
Taking the square root of both sides, we get:
r = √(59 / ((40/360) × 3.14))
Calculating this expression, we find that the radius of the circle is approximately 4.17 inches.
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