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Circle O shown below has a radius of 26 inches. Find, to the nearest tenth of a degree, the measure of the angle, x, that forms an arc whose length is 44 inches. Answer:

Circle O O shown below has a radius of 2626 inches. Find, to the nearest tenth of a a degree, the measure of the angle, x x , that forms an arc whose length is 4444 inches.\newlineAnswer: □∘ \square^{\circ}

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Full solution

Q. Circle O O shown below has a radius of 2626 inches. Find, to the nearest tenth of a a degree, the measure of the angle, x x , that forms an arc whose length is 4444 inches.\newlineAnswer: □∘ \square^{\circ}
  1. Use Arc Length Formula: To find the measure of angle x that corresponds to an arc length of 4444 inches on a circle with a radius of 2626 inches, we can use the formula for arc length: arc length=r×θ arc \ length = r \times \theta , where r is the radius and θ \theta is the angle in radians.
  2. Convert Radians to Degrees: First, we need to convert the angle from radians to degrees since the question asks for the answer in degrees. The conversion factor is 180π \frac{180}{\pi} degrees per radian.
  3. Solve for Theta: We can rearrange the arc length formula to solve for θ \theta in radians: θ=arc lengthr \theta = \frac{arc \ length}{r} .
  4. Substitute Values: Substitute the given values into the formula: θ=44 inches26 inches \theta = \frac{44 \ inches}{26 \ inches} .
  5. Calculate Radians: Calculate the value of θ \theta in radians: θ=4426≈1.6923 \theta = \frac{44}{26} \approx 1.6923 radians.
  6. Convert to Degrees: Now convert θ \theta from radians to degrees: θ×180π≈1.6923×180π≈96.9231 \theta \times \frac{180}{\pi} \approx 1.6923 \times \frac{180}{\pi} \approx 96.9231 degrees.
  7. Round to Nearest Tenth: Round the answer to the nearest tenth of a degree: θ≈96.9 \theta \approx 96.9 degrees.

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