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Circle O shown below has a radius of 3 inches. To the nearest tenth of an inch, determine the length of the arc, x, subtended by an angle of 70^(@). Answer: inches

Circle O O shown below has a radius of 33 inches. To the nearest tenth of an inch, determine the length of the arc, x x , subtended by an angle of 70∘ 70^{\circ} .\newlineAnswer: □\square inches

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Full solution

Q. Circle O O shown below has a radius of 33 inches. To the nearest tenth of an inch, determine the length of the arc, x x , subtended by an angle of 70∘ 70^{\circ} .\newlineAnswer: □\square inches
  1. Identify Formula: Identify the formula to calculate the length of an arc.\newlineThe length of an arc LL in a circle is given by the formula L=(θ/360)×2πrL = (\theta/360) \times 2\pi r, where θ\theta is the central angle in degrees and rr is the radius of the circle.
  2. Plug Values: Plug the given values into the formula.\newlineHere, θ=70\theta = 70 degrees and r=3r = 3 inches. So, L=(70360)⋅2⋅π⋅3L = \left(\frac{70}{360}\right) \cdot 2 \cdot \pi \cdot 3.
  3. Calculate Fraction: Calculate the fraction of the circle that the arc length represents. 70360\frac{70}{360} simplifies to 736.\frac{7}{36}.
  4. Calculate Arc Length: Calculate the arc length using the simplified fraction. L=(736)×2×π×3L = \left(\frac{7}{36}\right) \times 2 \times \pi \times 3. We know that π\pi is approximately 3.141593.14159.
  5. Perform Multiplication: Perform the multiplication to find the arc length.\newlineL=(736)×2×3.14159×3≈(736)×18.84954≈3.6659L = \left(\frac{7}{36}\right) \times 2 \times 3.14159 \times 3 \approx \left(\frac{7}{36}\right) \times 18.84954 \approx 3.6659 inches.
  6. Round Result: Round the result to the nearest tenth of an inch.\newlineThe length of the arc, to the nearest tenth, is approximately 3.73.7 inches.

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