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Answer :
To find the length of an arc on a circle intercepted by a central angle, you can use the formula for arc length, which is:
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the circle,
- [tex]\( \theta \)[/tex] is the central angle in radians.
For Exercise 97, we're given:
- Radius [tex]\( r = 14 \)[/tex] inches,
- Central angle [tex]\( \theta = \pi \)[/tex] radians.
Let's calculate the arc length step by step:
1. Identify the values:
- Radius [tex]\( r = 14 \)[/tex] inches.
- Central angle [tex]\( \theta = \pi \)[/tex] radians.
2. Apply the formula:
[tex]\[
\text{Arc Length} = 14 \times \pi
\][/tex]
3. Calculate the arc length:
- Multiply the radius by the central angle.
- This results in an arc length of approximately [tex]\( 43.98 \)[/tex] inches.
So, the length of the arc is approximately [tex]\( 43.98 \)[/tex] inches.
[tex]\[ \text{Arc Length} = r \times \theta \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the circle,
- [tex]\( \theta \)[/tex] is the central angle in radians.
For Exercise 97, we're given:
- Radius [tex]\( r = 14 \)[/tex] inches,
- Central angle [tex]\( \theta = \pi \)[/tex] radians.
Let's calculate the arc length step by step:
1. Identify the values:
- Radius [tex]\( r = 14 \)[/tex] inches.
- Central angle [tex]\( \theta = \pi \)[/tex] radians.
2. Apply the formula:
[tex]\[
\text{Arc Length} = 14 \times \pi
\][/tex]
3. Calculate the arc length:
- Multiply the radius by the central angle.
- This results in an arc length of approximately [tex]\( 43.98 \)[/tex] inches.
So, the length of the arc is approximately [tex]\( 43.98 \)[/tex] inches.
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