Circle O shown below has an arc of length 5 inches subtended by an angle of 103^(@). Find the length of the radius, x, to the nearest tenth of an inch. Answer: inches

Convert to Radians: To find the length of the radius, 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. First, we need to convert the angle from degrees to radians.Calculate Radians: To convert degrees to radians, we use the conversion factor $ \frac{\pi}{180} $. So, $ 103^{\circ} \times \frac{\pi}{180} $ radians is the angle in radians.Find Radius Formula: Performing the calculation: $ 103 \times \frac{\pi}{180} = \frac{103\pi}{180} $ radians.Substitute Values: Now we can use the formula for the arc length with the angle in radians to find the radius. Rearranging the formula to solve for $ r $, we get $ r = \frac{L}{\theta} $.Perform Calculation: Substitute the known values into the formula: $ r = \frac{5 \text{ inches}}{\frac{103\pi}{180}} $.Calculate Numerical Value: Perform the calculation: $ r = \frac{5 \times 180}{103\pi} $ inches.Approximate Pi: Using a calculator to find the numerical value: $ r \approx \frac{900}{103\pi} $ inches.Final Calculation: Approximating $ \pi $ as 3.14159 and performing the division: $ r \approx \frac{900}{324.07977} $ inches.Round Result: Final calculation gives: $ r \approx 2.775 $ inches.Round the result to the nearest tenth of an inch: $ r \approx 2.8 $ inches.

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Circle
O shown below has an arc of length 5 inches subtended by an angle of
103^(@).
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 $5$ inches subtended by an angle of $103^{\circ}$ . $\newline$ 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

5

inches subtended by an angle of

103^{\circ}

\newline

Find the length of the radius,

x

, to the nearest tenth of an inch.

\newline

Answer:

\square

inches

Convert to Radians: To find the length of the radius, 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. First, we need to convert the angle from degrees to radians.
Calculate Radians: To convert degrees to radians, we use the conversion factor $\frac{\pi}{180}$ . So, $103^{\circ} \times \frac{\pi}{180}$ radians is the angle in radians.
Find Radius Formula: Performing the calculation: $103 \times \frac{\pi}{180} = \frac{103\pi}{180}$ radians.
Substitute Values: Now we can use the formula for the arc length with the angle in radians to find the radius. Rearranging the formula to solve for $r$ , we get $r = \frac{L}{\theta}$ .
Perform Calculation: Substitute the known values into the formula: $r = \frac{5 \text{ inches}}{\frac{103\pi}{180}}$ .
Calculate Numerical Value: Perform the calculation: $r = \frac{5 \times 180}{103\pi}$ inches.
Approximate Pi: Using a calculator to find the numerical value: $r \approx \frac{900}{103\pi}$ inches.
Final Calculation: Approximating $\pi$ as $3$ . $14159$ and performing the division: $r \approx \frac{900}{324.07977}$ inches.
Round Result: Final calculation gives: $r \approx 2.775$ inches.
Round Result: Final calculation gives: $r \approx 2.775$ inches.Round the result to the nearest tenth of an inch: $r \approx 2.8$ inches.