To find the length of the minor arc SV in circle T, we can use the formula for arc length, which is:
Arc Length = r * θ
Where r is the radius of the circle and θ is the central angle in radians.
In this case, the radius r is 24 inches, and the central angle θ is 8 5π/6 radians.
First, let’s convert the angle:
8 5π/6 can be rewritten as:
8 + 5π/6
To use the formula, we need to calculate:
Arc Length = 24 * (8 + 5π/6)
Next, we calculate:
Arc Length = 24 * 8 + 24 * (5π/6)
Arc Length = 192 + 20π
Thus, the length of the minor arc SV is approximately:
Arc Length ≈ 192 + 62.83 ≈ 254.83 inches (using π ≈ 3.14)
So, the final answer is:
Minor Arc SV Length: 192 + 20π inches