Final answer:
To find the radius of a circle from an arc length of 15.0 cm and a subtended angle of 128°, convert the angle to radians and use the arc length formula, leading to a simple division to solve for the radius.
Step-by-step explanation:
Calculating the Radius of a Circle from Arc Length and Central Angle
The problem given involves finding the radius of a circle given an arc length and the measure of the central angle subtended by that arc. In this scenario, an arc length of 15.0 cm subtends a central angle of 128°. To find the radius, we use the formula that relates arc length (ℓ), radius (r), and central angle (in radians):
ℓ = r × θ
It is important to remember that angle should be in radians when using this formula. To convert degrees to radians, multiply by π/180. For 128°, the radians would be:
θ = 128° × (π/180°) = 128π/180
Now, replacing the arc length and the angle in radians into the formula, we can solve for r:
15.0 cm = r × (128π/180)
So,
r = 15.0 cm / (128π/180) = (15.0 × 180) / (128π) cm
Calculating this gives us the radius of the circle in centimeters. Therefore, the radius can be found by performing the division, which results in the answer.