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Circle
O shown below has a radius of 4 inches. To the nearest tenth of an inch, determine the length of the arc,
x, subtended by an angle of
139^(@).
Answer: inches

Circle $O$ shown below has a radius of $4$ inches. To the nearest tenth of an inch, determine the length of the arc, $x$ , subtended by an angle of $139^{\circ}$ . $\newline$ Answer: $\square$ inches

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Circles: word problems

Full solution

Q. Circle

O

shown below has a radius of

4

inches. To the nearest tenth of an inch, determine the length of the arc,

x

, subtended by an angle of

139^{\circ}

.

\newline

Answer:

\square

inches

Understand Relationship: Understand the relationship between the angle subtended by an arc and the length of the arc. $\newline$ The length of an arc $L$ in a circle is given by the formula $L = (\theta/360) \times 2\pi r$ , where $\theta$ is the angle in degrees and $r$ is the radius of the circle.
Identify Values: Identify the given values. $\newline$ We are given the radius $r$ of the circle as $4$ inches and the angle $\theta$ subtended by the arc as $139$ degrees.
Plug Given Values: Plug the given values into the arc length formula. $\newline$ Using the formula $L = (\theta/360) \times 2\pi r$ , we substitute $\theta = 139$ degrees and $r = 4$ inches. $\newline$ $L = (139/360) \times 2 \times \pi \times 4$
Calculate Arc Length: Calculate the arc length. $\newline$ We can use the approximation $\pi \approx 3.14$ to find the length of the arc. $\newline$ $L = (\frac{139}{360}) \times 2 \times 3.14 \times 4$ $\newline$ $L \approx (\frac{139}{360}) \times 25.12$
Perform Multiplication: Perform the multiplication and division to find the length of the arc. $\newline$ $L \approx (\frac{139}{360}) \times 25.12$ $\newline$ $L \approx 9.73333333333 \times 25.12$ $\newline$ $L \approx 244.5488$
Round Result: Round the result to the nearest tenth of an inch as requested. $\newline$ $L \approx 244.5$ tenths of an inch $\newline$ Since we are working in inches, we need to convert tenths of an inch back to inches by dividing by $10$ . $\newline$ $L \approx 24.45$ inches

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