To find the area of a sector given the arc length and radius, we first need to determine the angle in radians of the sector.
The formula for arc length (s) in terms of the radius (r) and angle (θ in radians) is:
s = r * θ
Given that the arc length (s) is 60 inches and the radius (r) is 15 inches, we can rearrange the formula to solve for θ:
θ = s / r
Plugging in the values:
θ = 60 in / 15 in = 4 radians
Now, we can use the angle to find the area (A) of the sector. The formula for the area of a sector based on the radius and the angle in radians is:
A = (1/2) * r² * θ
Substituting the known values into this formula:
A = (1/2) * (15 in)² * 4 radians
A = (1/2) * 225 in² * 4 = 450 in²
Therefore, the area of the sector is 450 square inches.