Find the area of the sector, given a central angle of 55degrees and a radius of 5.7 in. Round your answer to the nearest tenth.
Area K = 1/2 r^2 * angle in rads
Convert deg to rads
55 deg * pi/180 = 55pi/180 = 11pi/36 rads
11pi/36 rads = .96 rads
K = 1/2 (5.7)^2 * .96
K = ?
To find the area of the sector, you can use the formula:
Area = (θ/360) * π * r^2
Where:
θ = central angle in degrees
r = radius of the sector
In this case, the central angle is 55 degrees and the radius is 5.7 inches. Plugging these values into the formula:
Area = (55/360) * π * (5.7^2)
Calculating the area:
Area ≈ (0.1528) * 3.1416 * (32.49)
≈ 1.4965 square inches
Rounded to the nearest tenth, the area of the sector is approximately 1.5 square inches.