answer:
To find the area of the sector determined by an arc with a measure of 50° in a circle with a radius of 10, we can use the formula for the area of a sector:
Area of Sector = (θ/360°) * π * r^2
where θ is the central angle in degrees, π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
Plugging in the given values:
θ = 50°
r = 10
Area of Sector = (50°/360°) * 3.14159 * (10)^2
Area of Sector ≈ (0.1389) * 3.14159 * 100
Area of Sector ≈ 43.98 square units
Rounded to the nearest tenth, the area of the sector determined by the 50° arc in a circle with a radius of 10 is approximately 44.0 square units.