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Circle O shown below has a radius of 11 inches. Find, to the nearest tenth, the radian measure of the angle, x, that forms an arc whose length is 26 inches. Answer: radians

Circle O O shown below has a radius of 1111 inches. Find, to the nearest tenth, the radian measure of the angle, x x , that forms an arc whose length is 2626 inches.\newlineAnswer: □\square radians

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Q. Circle O O shown below has a radius of 1111 inches. Find, to the nearest tenth, the radian measure of the angle, x x , that forms an arc whose length is 2626 inches.\newlineAnswer: □\square radians
  1. Understand Relationship: Understand the relationship between arc length, radius, and central angle in radians. The formula that relates arc length ss, radius rr, and central angle in radians θ\theta is s=rθs = r\theta.
  2. Plug in Values: Plug in the given values into the formula.\newlineWe are given the arc length s=26s = 26 inches and the radius r=11r = 11 inches. We need to find the central angle in radians, θ\theta.\newlineSo, we have 26=11θ26 = 11\theta.
  3. Solve for θ\theta: Solve for θ\theta.\newlineTo find θ\theta, we divide both sides of the equation by 1111.\newlineθ=2611\theta = \frac{26}{11}\newlineθ≈2.36363636...\theta \approx 2.36363636...
  4. Round Result: Round the result to the nearest tenth.\newlineRounding θ\theta to the nearest tenth gives us θ≈2.4\theta \approx 2.4 radians.

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