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Circle
O shown below has a radius of 8 inches. To the nearest tenth of an inch, determine the length of the arc,
x, subtended by an angle of
136^(@).
Answer: inches

Circle $O$ shown below has a radius of $8$ inches. To the nearest tenth of an inch, determine the length of the arc, $x$ , subtended by an angle of $136^{\circ}$ . $\newline$ Answer: $\square$ inches

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Circles: word problems

Full solution

Q. Circle

O

shown below has a radius of

8

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

x

, subtended by an angle of

136^{\circ}

.

\newline

Answer:

\square

inches

Understand Relationship: Understand the relationship between the angle subtended by an arc, the radius of the circle, and the length of the arc. $\newline$ The formula to find the length of an arc $s$ is $s = r\theta$ , where $r$ is the radius and $\theta$ is the angle in radians. $\newline$ To convert degrees to radians, we use the conversion factor $\pi$ radians $= 180$ degrees.
Convert to Radians: Convert the angle from degrees to radians. $\newline$ We have an angle of $136$ degrees. To convert it to radians, we multiply by $\pi/180$ . $\newline$ $\theta$ in radians = $136 \times (\pi/180)$ .
Calculate Angle: Calculate the angle in radians. $\newline$ $\theta$ in radians = $136 \times (\pi/180) = \frac{136\pi}{180}$ . $\newline$ We can simplify this fraction by dividing both the numerator and the denominator by $4$ . $\newline$ $\theta$ in radians = $(136/4)\pi/(180/4) = \frac{34\pi}{45}$ .
Use Arc Length Formula: Use the formula for the arc length with the radius and the angle in radians. $\newline$ We know the radius $r$ is $8$ inches and $\theta$ in radians is $\frac{34\pi}{45}$ . $\newline$ Arc length $s$ = $r\theta = 8 \times \left(\frac{34\pi}{45}\right)$ .
Calculate Arc Length: Calculate the arc length. $\newline$ Arc length $s$ = $8 \times (34\pi/45)$ = $(8 \times 34\pi)/45$ = $272\pi/45$ .
Evaluate Using Approximation: Evaluate the arc length using the approximation for $\pi$ ( $\pi \approx 3.14$ ). $\newline$ Arc length (s) $\approx (272 \times 3.14)/45$ .
Perform Multiplication and Division: Perform the multiplication and division to find the arc length. Arc length $s$ $\approx$ $\frac{854.88}{45}$ $\approx$ $18.9973333$ inches.
Round to Nearest Tenth: Round the arc length to the nearest tenth of an inch. $\newline$ Arc length $s$ $\approx 19.0$ inches.

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\newline

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\newline

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\newline

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\newline

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Question

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and a base with a diameter of

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\newline

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