Final answer:
To find the arc length the windshield wiper blade sweeps out, one must convert the angle to radians and use the formula L = r × θ. In this example, the wiper blade and arm have a total length of 30 inches and sweep out an angle of 125 degrees, resulting in an approximate arc length of 65.49 inches.
Step-by-step explanation:
The student's question involves calculating the arc length swept out by a windshield wiper blade that forms part of a circle. Given that the wiper blade is 24 inches long and together with the arm has a total length of 30 inches, and it sweeps out an angle of 125 degrees, we can use the formula for the arc length of a circle, L = r × θ, where L is the arc length, r is the radius (in this case, the total length of the arm and blade), and θ is the central angle in radians.
To find the arc length in this scenario, we first need to convert the angle from degrees to radians by multiplying by π / 180°. Once we have the angle in radians, we multiply by the total length of the wiper to find the arc length. The radius, r, is 30 inches, and the angle, θ, is 125 degrees (≈ 2.183 radians). Therefore, the arc length L would be 30 inches × 2.183 radians = 65.49 inches (approximately).