Circle O shown below has an arc of length 46 inches subtended by an angle of 136^(@). Find the length of the radius, x, to the nearest tenth of an inch. Answer: inches

Identify Formula: Identify the formula that relates the arc length, the central angle in radians, and the radius of the circle. The formula is: Arc length = Radius × Central angle (in radians) To use this formula, we need to convert the central angle from degrees to radians.Convert to Radians: Convert the central angle from degrees to radians. We use the conversion factor that π radians = 180 degrees. 136 degrees × (π radians / 180 degrees) = (136π / 180) radiansPlug Values: Plug the values into the arc length formula. We have the arc length (46 inches) and the central angle in radians ((136π / 180) radians), and we need to find the radius (x). 46 = x × (136π / 180)Solve for Radius: Solve for the radius (x). To isolate x, we divide both sides of the equation by (136π / 180). x = 46 / (136π / 180)Perform Division: Perform the division to find the value of x. x = 46 / (136π / 180) = (46 × 180) / (136π) = 8280 / (136π)Calculate Value: Calculate the numerical value of x. x ≈ 8280 / (136 × 3.14159) ≈ 8280 / 427.25664 ≈ 19.38Round to Nearest: Round the value of x to the nearest tenth of an inch. x ≈ 19.4 inches

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Circle
O shown below has an arc of length 46 inches subtended by an angle of
136^(@).
Find the length of the radius,
x, to the nearest tenth of an inch.
Answer: inches

Circle $O$ shown below has an arc of length $46$ inches subtended by an angle of $136^{\circ}$ . $\newline$ Find the length of the radius, $x$ , to the nearest tenth of an inch. $\newline$ Answer: $\square$ inches

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Grade 8

Circles: word problems

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Q. Circle

O

shown below has an arc of length

46

inches subtended by an angle of

136^{\circ}

\newline

Find the length of the radius,

x

, to the nearest tenth of an inch.

\newline

Answer:

\square

inches

Identify Formula: Identify the formula that relates the arc length, the central angle in radians, and the radius of the circle. $\newline$ The formula is: Arc length = Radius $\times$ Central angle (in radians) $\newline$ To use this formula, we need to convert the central angle from degrees to radians.
Convert to Radians: Convert the central angle from degrees to radians. $\newline$ We use the conversion factor that $\pi$ radians = $180$ degrees. $\newline$ $136$ degrees $\times$ ( $\pi$ radians / $180$ degrees) = ( $136\pi / 180$ ) radians
Plug Values: Plug the values into the arc length formula. $\newline$ We have the arc length ( $46$ inches) and the central angle in radians ( $\frac{136\pi}{180}$ radians), and we need to find the radius ( $x$ ). $\newline$ $46 = x \times \left(\frac{136\pi}{180}\right)$
Solve for Radius: Solve for the radius $x$ . To isolate $x$ , we divide both sides of the equation by $(136\pi / 180)$ . $x = 46 / (136\pi / 180)$
Perform Division: Perform the division to find the value of $x$ . $x = \frac{46}{\frac{136\pi}{180}} = \frac{46 \times 180}{136\pi} = \frac{8280}{136\pi}$
Calculate Value: Calculate the numerical value of $x$ . $x \approx \frac{8280}{(136 \times 3.14159)} \approx \frac{8280}{427.25664} \approx 19.38$
Round to Nearest: Round the value of $x$ to the nearest tenth of an inch. $x \approx 19.4$ inches