Find the measure of the central angle, in radians, given the area of the sector as
22.6 cm2 and a radius equal to 3.7 cm. Round your answer to the nearest tenth.
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To find the measure of the central angle in radians, we can use the formula:
Area of sector = (θ/2π) × πr²
where θ is the measure of the central angle in radians, and r is the radius.
Given that the area of the sector is 22.6 cm² and the radius is 3.7 cm, we can rearrange the formula to solve for θ:
22.6 = (θ/2π) × π(3.7)²
Simplifying the equation, we have:
22.6 = (θ/2) × (3.7)²
22.6 = (θ/2) × 13.69
Dividing both sides by 13.69, we get:
22.6/13.69 = θ/2
θ/2 = 1.653627
Multiplying both sides by 2 to isolate θ, we have:
θ = 1.653627 × 2
θ ≈ 3.307254
Rounding to the nearest tenth, the measure of the central angle in radians is approximately 3.3 radians.