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Circle O shown below has a radius of 25 inches. Find, to the nearest tenth, the radian measure of the angle, x, that forms an arc whose length is 18 inches. Answer: radians

Circle O O shown below has a radius of 2525 inches. Find, to the nearest tenth, the radian measure of the angle, x x , that forms an arc whose length is 1818 inches.\newlineAnswer: □\square radians

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Q. Circle O O shown below has a radius of 2525 inches. Find, to the nearest tenth, the radian measure of the angle, x x , that forms an arc whose length is 1818 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=18s = 18 inches and the radius r=25r = 25 inches. We need to find the angle θ\theta in radians.\newlineSo, 18=25θ18 = 25\theta.
  3. Solve for θ\theta: Solve for θ\theta.\newlineTo find θ\theta, we divide both sides of the equation by 2525.\newlineθ=1825\theta = \frac{18}{25}.
  4. Calculate θ\theta: Calculate the value of θ\theta.θ=1825=0.72\theta = \frac{18}{25} = 0.72 radians.
  5. Round Answer: Round the answer to the nearest tenth. θ≈0.7\theta \approx 0.7 radians (to the nearest tenth).

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