Final answer:
To find the radius of a circle given an arc length of 98 cm and an angle of 120°, convert the angle to radians and use the arc length formula. The calculated radius is approximately 46.77 cm.
Step-by-step explanation:
The student has asked about finding the radius of a circle given that an angle of 120° subtends an arc length of 98 cm. To solve this, we use the relationship between the arc length (s), the radius (r), and the central angle in radians (θ), which is s = rθ. First, we need to convert the central angle from degrees to radians by multiplying it with π/180. So, the angle in radians is 120° × (π/180) = 2π/3 rad.
Substituting the given values into the formula, we have:
98 cm = r × (2π/3)
To find the radius (r), we divide the arc length by the angle in radians:
r = 98 cm / (2π/3)
After calculating this, we find that the radius of the circle is approximately 46.77 cm.