An amusement park has discovered that the brace that provides stability to the Ferris wheel has been damaged and needs work. The arc length of the steel reinforcement that must be replaced is between the two seats shown below. The sector area is 28.25 ft2 and the radius is 12 feet. What is the length of steel that must be replaced (Arc Length)?

4.71 Feet

Step-by-step explanation:

According to the Question,

Given That, An amusement park has discovered that the brace that provides stability to the Ferris wheel has been damaged and needs work. The arc length of the steel reinforcement that must be replaced is between the two seats. The sector area is 28.25 ft² and the radius is 12 feet.

We have, Area of Sector = 28.25 ft² & Radius = 12 feet

We Know, Area of sector = ∅/360 × π × r²

Put the values,

28.25 = ∅/360 × π × 12²

∅ = (28.25 × 360) / π×12²

∅ = 22.47 ≈ 22.5

And, length of arc =  ∅/360 × 2 × π × r

L =  22.5/360 × 2 × π × 12

L = 4.71 Feet