The area of a sector is 52 in2. If the radius is 10 in, what is the measure of the angle of the sector?
Question
The area of a sector is 52 in². If the radius is 10 in, what is the measure of the angle of the sector?
Solution
The formula for the area of a sector is given by:
Area = (θ/360) * π * r²
where: θ is the angle of the sector, r is the radius of the circle.
Given that the area is 52 in² and the radius is 10 in, we can substitute these values into the formula and solve for θ:
52 = (θ/360) * π * 10²
Solving this equation for θ gives:
θ = (52 * 360) / (π * 10²)
Calculating this gives:
θ ≈ 59.24 degrees
So, the measure of the angle of the sector is approximately 59.24 degrees.
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