Circle O shown below has an arc of length 30 inches subtended by an angle of 63^(@). Find the length of the radius, x, to the nearest tenth of an inch. Answer: inches

Convert degrees to radians: To find the radius of the circle, we can use the formula for the length of an arc, which is $ L = r\theta $, where $ L $ is the arc length, $ r $ is the radius, and $ \theta $ is the central angle in radians. Since we have the angle in degrees, we need to convert it to radians first.Calculate angle in radians: To convert degrees to radians, we use the conversion factor $ \frac{\pi}{180} $. So, $ 63 $ degrees is $ 63 \times \frac{\pi}{180} $ radians.Use arc length formula: Now, let's calculate the angle in radians: $ 63 \times \frac{\pi}{180} = \frac{63}{180} \times \pi \approx 1.1 $ radians (using $ \pi \approx 3.14 $).Calculate radius: With the angle in radians, we can now use the arc length formula $ L = r\theta $ to find the radius. We have $ L = 30 $ inches and $ \theta \approx 1.1 $ radians. We need to solve for $ r $: $ r = \frac{L}{\theta} $.Round to nearest tenth: Plugging in the values, we get $ r = \frac{30}{1.1} $. Let's calculate this value.The calculation gives us $ r \approx 27.3 $ inches. However, we need to round this to the nearest tenth of an inch.Rounding $ 27.3 $ inches to the nearest tenth gives us $ 27.3 $ inches, as it is already at the tenth place.

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Circle
O shown below has an arc of length 30 inches subtended by an angle of
63^(@).
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 $30$ inches subtended by an angle of $63^{\circ}$ . $\newline$ Find the length of the radius, $x$ , to the nearest tenth of an inch. $\newline$ Answer: $\square$ inches

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Q. Circle

O

shown below has an arc of length

30

inches subtended by an angle of

63^{\circ}

\newline

Find the length of the radius,

x

, to the nearest tenth of an inch.

\newline

Answer:

\square

inches

Convert degrees to radians: To find the radius of the circle, we can use the formula for the length of an arc, which is $L = r\theta$ , where $L$ is the arc length, $r$ is the radius, and $\theta$ is the central angle in radians. Since we have the angle in degrees, we need to convert it to radians first.
Calculate angle in radians: To convert degrees to radians, we use the conversion factor $\frac{\pi}{180}$ . So, $63$ degrees is $63 \times \frac{\pi}{180}$ radians.
Use arc length formula: Now, let's calculate the angle in radians: $63 \times \frac{\pi}{180} = \frac{63}{180} \times \pi \approx 1.1$ radians (using $\pi \approx 3.14$ ).
Calculate radius: With the angle in radians, we can now use the arc length formula $L = r\theta$ to find the radius. We have $L = 30$ inches and $\theta \approx 1.1$ radians. We need to solve for $r$ : $r = \frac{L}{\theta}$ .
Round to nearest tenth: Plugging in the values, we get $r = \frac{30}{1.1}$ . Let's calculate this value.
Round to nearest tenth: Plugging in the values, we get $r = \frac{30}{1.1}$ . Let's calculate this value.The calculation gives us $r \approx 27.3$ inches. However, we need to round this to the nearest tenth of an inch.
Round to nearest tenth: Plugging in the values, we get $r = \frac{30}{1.1}$ . Let's calculate this value.The calculation gives us $r \approx 27.3$ inches. However, we need to round this to the nearest tenth of an inch.Rounding $27.3$ inches to the nearest tenth gives us $27.3$ inches, as it is already at the tenth place.