Give three points of a triangle and get all angles and side lengths

triangle_info.R

triangle_info <- function(A, B, C) {
  # Helper function to compute distance between two points
  dist <- function(P, Q) sqrt((P[1] - Q[1])^2 + (P[2] - Q[2])^2)
  
  # Side lengths
  dist_AB <- dist(A, B)
  dist_AC <- dist(A, C)
  dist_BC <- dist(B, C)
  
  # Law of Cosines for each angle
  angle_A <- acos((dist_AB^2 + dist_AC^2 - dist_BC^2) / (2 * dist_AB * dist_AC)) * 180 / pi
  angle_B <- acos((dist_AB^2 + dist_BC^2 - dist_AC^2) / (2 * dist_AB * dist_BC)) * 180 / pi
  angle_C <- acos((dist_AC^2 + dist_BC^2 - dist_AB^2) / (2 * dist_AC * dist_BC)) * 180 / pi
  
  return(list(
    angle_A = angle_A,
    angle_B = angle_B,
    angle_C = angle_C,
    dist_AB = dist_AB,
    dist_AC = dist_AC,
    dist_BC = dist_BC
  ))
}

# Example usage:
A <- c(0, 0)
B <- c(1, 0)
C <- c(0, 1)
triangle_info(A, B, C)