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Circle
O shown below has a radius of 11 inches. To the nearest tenth of an inch, determine the length of the arc,
x, subtended by an angle of
145^(@).
Answer: inches

Circle $O$ shown below has a radius of $11$ inches. To the nearest tenth of an inch, determine the length of the arc, $x$ , subtended by an angle of $145^{\circ}$ . $\newline$ Answer: $\square$ inches

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Circles: word problems

Full solution

Q. Circle

O

shown below has a radius of

11

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

x

, subtended by an angle of

145^{\circ}

.

\newline

Answer:

\square

inches

Identify formula: Identify the formula to calculate the length of an 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 central angle in degrees and $r$ is the radius of the circle.
Plug values: Plug in the given values into the formula. $\newline$ Here, $\theta = 145$ degrees and $r = 11$ inches. Using the approximation $\pi \approx 3.14$ , we can calculate the length of the arc. $\newline$ $L = (\frac{145}{360}) \times 2 \times 3.14 \times 11$
Calculate arc length: Calculate the length of the arc. $\newline$ First, calculate the fraction of the circle that the arc covers by dividing the angle by $360$ degrees. $\newline$ $\frac{145}{360} \approx 0.4028$ (rounded to four decimal places for precision in intermediate steps) $\newline$ Now, multiply this fraction by the circumference of the entire circle $(2 \cdot \pi \cdot r)$ . $\newline$ $L \approx 0.4028 \cdot 2 \cdot 3.14 \cdot 11$
Perform multiplication: Perform the multiplication to find the length of the arc. $\newline$ $L \approx 0.4028 \times 2 \times 3.14 \times 11$ $\newline$ $L \approx 0.4028 \times 69.08$ (since $2 \times 3.14 \times 11 = 69.08$ ) $\newline$ $L \approx 27.8264$ inches
Round result: Round the result to the nearest tenth of an inch as the problem asks. $\newline$ $L \approx 27.8$ inches (rounded to the nearest tenth)

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