Final answer:
To calculate the end-to-center distance of an 8" long radius 45-degree elbow, use the arc length formula x = rθ with θ in radians. The resulting distance is approximately 6.28 inches.
Step-by-step explanation:
To calculate the distance from the end to the center for an 8" long radius 45-degree elbow, we can use the arc length formula, which is x = rθ. For a 45-degree elbow, the angle θ is 45 degrees, which needs to be converted to radians by multiplying by π/180. Therefore, θ = 45 * (π/180) radians, and since r (the radius) is 8 inches, the calculation is:
x = 8" * (45 * (π/180))
After performing the calculation:
x = 8" * π/4
x ≈ 8" * 0.785
x ≈ 6.28 inches
The distance from the end to the center of an 8" long radius 45-degree elbow is approximately 6.28 inches. Note that we use two significant figures for the final answer because the radius is given to two significant figures.