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Circle O shown below has an arc of length 48 inches subtended by an angle of 1.6 radians. Find the length of the radius, x, to the nearest tenth of an inch. Answer: inches

Circle O O shown below has an arc of length 4848 inches subtended by an angle of 11.66 radians. Find the length of the radius, x x , to the nearest tenth of an inch.\newlineAnswer: □\square inches

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Full solution

Q. Circle O O shown below has an arc of length 4848 inches subtended by an angle of 11.66 radians. Find the length of the radius, x x , to the nearest tenth of an inch.\newlineAnswer: □\square inches
  1. Use Arc Length Formula: To find the radius of the circle, we can use the formula for the length of an arc, which is arc length=radius×angle arc \ length = radius \times angle in radians. We need to rearrange the formula to solve for the radius.
  2. Rearrange Formula: The rearranged formula to solve for the radius (x) is radius=arc lengthangle radius = \frac{arc \ length}{angle} .
  3. Plug in Values: Now we can plug in the values we have: x=48 inches1.6 radians x = \frac{48 \ inches}{1.6 \ radians} .
  4. Perform Division: Performing the division gives us x=481.6 x = \frac{48}{1.6} .
  5. Calculate Result: Calculating the division, we get x=30 x = 30 inches.
  6. Round to Nearest Tenth: We need to round the result to the nearest tenth of an inch. Since the result is a whole number, it is already to the nearest tenth.

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