• TheOakTree@beehaw.org
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      8 months ago

      (1/2)×θ×r^2

      is the area of a circle sector, like a slice of pie.

      (1/2)×sin(θ)×side1×side2

      is the side-angle-side formula for the area of a triangle.

      We know that the triangle encompassed by the sector has two sides that are equal to the radius, so we replace side1×side2 with r^2. Since the area of the arc segment is equal to the area of a sector minus the triangle, we can subtract triangle area from sector area to get

      (1/2)×(θ-sin(θ))×r^2

      which is the area of the arc segment, as shown with pie in the picture.