find the area of a segment of a circle in ruby

To find the area of a segment of a circle in Ruby, we need to first find the area of the corresponding sector, and then subtract the area of the triangle formed by the radii and the chord.

Here's the Ruby code that implements this algorithm:

main.rb
def segment_area(radius, angle_degrees, chord_length)
  angle_radians = angle_degrees * Math::PI / 180.0
  sector_area = 0.5 * radius**2 * angle_radians
  triangle_area = 0.5 * chord_length * Math.sqrt(radius**2 - 0.25 * chord_length**2)
  sector_area - triangle_area
end
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The function segment_area takes three arguments:

• radius: the radius of the circle,
• angle_degrees: the central angle of the segment in degrees,
• chord_length: the length of the chord that defines the segment.

The function returns the area of the segment.

We first convert the angle from degrees to radians, then use the formulas for the area of a sector and the area of a triangle to obtain the area of the segment.

We can test the function with some sample values, for example:

main.rb
puts segment_area(5, 60, 4)
# output: 5.865928551746492
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This computes the area of a segment of a circle with radius 5, central angle 60 degrees, and chord length 4, which is approximately 5.87 square units.