A Circle Has A Radius Of 5 Ft And An Arc Of Length 7 Ft Is Formed By The Intersection Of The Circle With A Central Angle. Which Equation Gives The Measure Of The Central Angle, $q$?A. $a = \frac{5}{7}$B. $q = \frac{7}{5}$C.
**A Circle with a Central Angle: Understanding the Relationship Between Arc Length and Central Angle**
What is the relationship between the arc length and the central angle of a circle?
The relationship between the arc length and the central angle of a circle is given by the formula:
Arc Length = (Central Angle / 360) × Circumference
Where:
- Arc Length is the length of the arc formed by the intersection of the circle with a central angle.
- Central Angle is the angle formed by the two radii that intersect at the center of the circle.
- Circumference is the distance around the circle.
How do we calculate the central angle of a circle given the arc length and radius?
To calculate the central angle of a circle given the arc length and radius, we can use the following formula:
Central Angle = (Arc Length / Radius) × 360
Where:
- Arc Length is the length of the arc formed by the intersection of the circle with a central angle.
- Radius is the distance from the center of the circle to the edge of the circle.
- 360 is the total number of degrees in a circle.
What is the equation that gives the measure of the central angle, q?
Given a circle with a radius of 5 ft and an arc of length 7 ft, we can use the formula above to calculate the central angle:
q = (7 / 5) × 360
q = 504
Therefore, the equation that gives the measure of the central angle, q, is:
q = (Arc Length / Radius) × 360
Q&A
Q: What is the relationship between the arc length and the central angle of a circle?
A: The relationship between the arc length and the central angle of a circle is given by the formula: Arc Length = (Central Angle / 360) × Circumference.
Q: How do we calculate the central angle of a circle given the arc length and radius?
A: To calculate the central angle of a circle given the arc length and radius, we can use the formula: Central Angle = (Arc Length / Radius) × 360.
Q: What is the equation that gives the measure of the central angle, q?
A: The equation that gives the measure of the central angle, q, is: q = (Arc Length / Radius) × 360.
Q: What is the measure of the central angle, q, for a circle with a radius of 5 ft and an arc of length 7 ft?
A: The measure of the central angle, q, for a circle with a radius of 5 ft and an arc of length 7 ft is: q = 504.
Q: What is the formula for calculating the arc length of a circle given the central angle and radius?
A: The formula for calculating the arc length of a circle given the central angle and radius is: Arc Length = (Central Angle / 360) × Circumference.
Q: What is the formula for calculating the central angle of a circle given the arc length and radius?
A: The formula for calculating the central angle of a circle given the arc length and radius is: Central Angle = (Arc Length / Radius) × 360.
Conclusion
In conclusion, the relationship between the arc length and the central angle of a circle is given by the formula: Arc Length = (Central Angle / 360) × Circumference. To calculate the central angle of a circle given the arc length and radius, we can use the formula: Central Angle = (Arc Length / Radius) × 360. The equation that gives the measure of the central angle, q, is: q = (Arc Length / Radius) × 360.