In circle K with m JKL=144 and JK=6 units, find the length of arc JL. Round to the nearest hundredth.
Transcribed Image Text:### Arc Length Problem
**Posted on**: Jun 10, 8:10:03 PM
#### Concept Overview
Arc length is a portion of the circumference of a circle, determined by the central angle subtending that arc.
#### Example Problem
Given the circle \( K \) and the measures:
- \( \angle JKL = 144^\circ \)
- \( JK = 6 \) units
Find the length of arc \( JL \). Round to the nearest hundredth.
- The circle has its center at point \( K \).
- Points \( J \) and \( L \) are on the circumference.
- Line segments \( JK \) and \( KL \) (radius lines) play a key role.
#### Explanation
1. **Determine the fraction of the circumference for the arc**: The angle \( \angle JKL \) is given in degrees, and since there are \( 360^\circ \) in a full circle:
\[
\text{Fraction of the circumference} = \frac{\angle JKL}{360} = \frac{144}{360} = \frac{2}{5} \quad \text{or} \quad 0.4
\]
2. **Find the circumference of the circle** using the radius:
\[
\text{Circumference} = 2 \pi r = 2 \pi \times 6 = 12 \pi \quad \text{units}
\]
3. **Calculate the arc length** \( JL \):
\[
\text{Arc Length JL} = \text{Fraction of the circumference} \times \text{Circumference} = 0.4 \times 12 \pi
\]
\[
\text{Arc Length JL} = 4.8 \pi \approx 15.08 \quad \text{units}
\]
Thus, the length of arc \( JL \) is approximately **15.08 units**.
Enter your calculated answer in the provided box.
**Answer**:
\[ \boxed{\_\_\_\_\_\_} \]
Submit your evaluated answer.
Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.
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- The circle has its center at point \( K \).
- Points \( J \) and \( L \) are on the circumference.
- Line segments \( JK \) and \( KL \) (radius lines) play a key role.
#### Explanation
1. **Determine the fraction of the circumference for the arc**: The angle \( \angle JKL \) is given in degrees, and since there are \( 360^\circ \) in a full circle:
\[
\text{Fraction of the circumference} = \frac{\angle JKL}{360} = \frac{144}{360} = \frac{2}{5} \quad \text{or} \quad 0.4
\]
2. **Find the circumference of the circle** using the radius:
\[
\text{Circumference} = 2 \pi r = 2 \pi \times 6 = 12 \pi \quad \text{units}
\]
3. **Calculate the arc length** \( JL \):
\[
\text{Arc Length JL} = \text{Fraction of the circumference} \times \text{Circumference} = 0.4 \times 12 \pi
\]
\[
\text{Arc Length JL} = 4.8 \pi \approx 15.08 \quad \text{units}
\]
Thus, the length of arc \( JL \) is approximately **15.08 units**.
Enter your calculated answer in the provided box.
**Answer**:
\[ \boxed{\_\_\_\_\_\_} \]
Submit your evaluated answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe768e832-4394-4037-9c96-0d66378e533e%2Fa759344f-2c17-4134-b7c3-3f49b44e562e%2Fv6bgzsl_processed.jpeg&w=3840&q=75)
