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GC.5 Arc Length Mini-Task: Use the Geometry Formula sheet to support your work. Consider a set of concentric circles, as shown below. 60 111 a. Complete the table below for the arc lengths of the 60° arcs. Leave your answers in terms of a. radius, r |arc length, s | 2 3 4 5 b. On the grid below, plot the points described in the table from part a. Connect the points with a line.

GC.5 Arc Length Mini-Task: Use the Geometry Formula sheet to support your work. Consider a set of concentric circles, as shown below. 60 111 a. Complete the table below for the arc lengths of the 60° arcs. Leave your answers in terms of a. radius, r |arc length, s | 2 3 4 5 b. On the grid below, plot the points described in the table from part a. Connect the points with a line.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**GC.5 Arc Length Mini-Task: Use the Geometry Formula Sheet to Support Your Work** Consider a set of concentric circles, as shown below. *Image Description:* A diagram shows concentric circles with a central angle of 60°. There is a radius line extending from the center to the circumference of the innermost circle, marked as 2. **Tasks:** a. Complete the table below for the arc lengths of the 60° arcs. Leave your answers in terms of π. | Radius, r | 2 | 3 | 4 | 5 | |-----------|---|---|---|---| | Arc Length, s | | | | | b. On the grid below, plot the points described in the table from part a. Connect the points with a line. *Instructions:* - Use the geometry formula sheet to calculate the arc length of each circle based on the given radii. - Arc length formula: \( s = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the central angle.
Transcribed Image Text:**GC.5 Arc Length Mini-Task: Use the Geometry Formula Sheet to Support Your Work** Consider a set of concentric circles, as shown below. *Image Description:* A diagram shows concentric circles with a central angle of 60°. There is a radius line extending from the center to the circumference of the innermost circle, marked as 2. **Tasks:** a. Complete the table below for the arc lengths of the 60° arcs. Leave your answers in terms of π. | Radius, r | 2 | 3 | 4 | 5 | |-----------|---|---|---|---| | Arc Length, s | | | | | b. On the grid below, plot the points described in the table from part a. Connect the points with a line. *Instructions:* - Use the geometry formula sheet to calculate the arc length of each circle based on the given radii. - Arc length formula: \( s = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the central angle.
The image displays a graph with a grid layout. The y-axis is labeled "s" and ranges from 0 to 7, while the x-axis is labeled "r" and also ranges from 0 to 7. This graph is likely used to represent a relationship between two variables, potentially involving circle properties given the context. Below the graph, there is a question: "c. What type of relationship exists between arc length and the radius of a circle?" **Graph Explanation** - The graph's axes suggest a linear scale for both the arc length (s) and radius (r). - Typically, the relationship between arc length (s) and radius (r) is linear for a fixed central angle, based on the formula \( s = r\theta \), where \(\theta\) is the angle in radians. This indicates that the arc length is directly proportional to the radius if the angle is constant. The educational content here may focus on understanding how changes in one variable affect the other within the context of circular measurements.
Transcribed Image Text:The image displays a graph with a grid layout. The y-axis is labeled "s" and ranges from 0 to 7, while the x-axis is labeled "r" and also ranges from 0 to 7. This graph is likely used to represent a relationship between two variables, potentially involving circle properties given the context. Below the graph, there is a question: "c. What type of relationship exists between arc length and the radius of a circle?" **Graph Explanation** - The graph's axes suggest a linear scale for both the arc length (s) and radius (r). - Typically, the relationship between arc length (s) and radius (r) is linear for a fixed central angle, based on the formula \( s = r\theta \), where \(\theta\) is the angle in radians. This indicates that the arc length is directly proportional to the radius if the angle is constant. The educational content here may focus on understanding how changes in one variable affect the other within the context of circular measurements.
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