Final answer:
To mark an arc with a 53-degree angle and a 12-foot radius, you first convert the angle to radians and then multiply by the radius to find the arc length. The arc length is approximately 11.09 feet.
Step-by-step explanation:
To find the length of the arc that needs to be marked with a 53 degrees angle and a radius of 12 feet, we can use the formula for arc length, given the radius (r) and the central angle in radians (Δθ):
Δs = r Δθ
First, we must convert the angle from degrees to radians. Since there are π radians in 180 degrees, the angle in radians is:
Δθ = 53 degrees × (π / 180 degrees) = 53π/180
Now, we can calculate the arc length (Δs):
Δs = 12 feet × (53π/180)
Δs = (12 × 53π) / 180 feet
Δs ≈ (636π) / 180 feet
Δs ≈ 3.53π feet
Δs ≈ 11.09 feet
Therefore, the length of the arc needed to be marked is approximately 11.09 feet.