Final answer:
The measurement of the central angle in degrees for a circle with a radius of 6 meters and an arc length of 5/2 π meters is calculated by dividing the arc length by the radius to find the angle in radians and then converting to degrees.
Step-by-step explanation:
The student is asking how to calculate the measurement of a central angle in degrees for a circle with a radius of 6 meters, when the arc length is 5/2 π meters. To find this, we use the relationship that the arc length (Δs) is equal to the radius (r) times the central angle (Δθ) in radians, expressed as Δs = r·Δθ. Since there are 2π radians in a full circle (360 degrees), we can convert the angle to degrees after finding it in radians.
We know that the circumference of the circle is 2πr and that a full circle (360 degrees) corresponds to the full circumference. If we take the arc length 5/2 π and divide it by the radius, 6 meters, we get the central angle in radians. We then multiply by (180/π) to convert to degrees.
Here's the calculation step-by-step:
Multiply by (180/π) to convert radians to degrees.
The resulting angle is the measurement of the central angle in degrees subtended by the given arc.