To find the radius using the arc length formula, we need to apply the formula for arc length, which is:
Arc Length (s) = r × θ
where:
- s is the arc length,
- r is the radius, and
- θ is the angle in radians.
In this case, we have:
- s = 16 cm
- θ = 48 degrees
Before we can use the formula, we need to convert the angle from degrees to radians because the formula requires the angle in radians. To convert degrees to radians, we use the conversion factor:
radians = degrees × (π / 180)
So, for 48 degrees:
θ = 48 × (π / 180) = 48π / 180 = 4π / 15 radians
Now, we can plug the values back into the arc length formula:
16 cm = r × (4π / 15)
To find r, we rearrange the equation:
r = 16 cm / (4π / 15)
This simplifies to:
r = 16 cm × (15 / 4π) = 60 / π cm
Now, if you need a numerical approximation, we can calculate:
r ≈ 19.1 cm (using π ≈ 3.14)
So, the radius r is approximately 19.1 cm when using the given arc length and angle.