import math

class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        
    def __str__(self):
        return f"P({self.x},{self.y})"
    
    def degree_at_angle(self, P2, P3):
        at1 = math.atan2(P3.y - self.y, P3.x - self.x)
        at2 = math.atan2(P2.y - self.y, P2.x - self.x)
        return abs(math.degrees(at1-at2))

def tan(deg):
    return math.tan(math.radians(deg))
    

AD_LENGTH = 1

A = Point(0,0)
D = Point(AD_LENGTH, 0)

_Bx = (AD_LENGTH * tan(4)) / (tan(10) + tan(4))
_By = _Bx * tan(10)

B = Point(_Bx, _By)

_Cx = (AD_LENGTH * tan(50)) / (tan(74) + tan(50))
_Cy = _Cx * tan(74)

C = Point(_Cx, _Cy)

print(A, B, C, D)
print("CAB", A.degree_at_angle(C, B))
print("BAD", A.degree_at_angle(D, B))
print("BDA", D.degree_at_angle(A, B))
print("BDC", D.degree_at_angle(C, B))
print("CAD", A.degree_at_angle(C, D))
print("CDA", D.degree_at_angle(C, A))
print("ACD", C.degree_at_angle(D, A))
print("ACB", C.degree_at_angle(B, A))
print("BCD", C.degree_at_angle(B, D))

"""
P(0,0) P(0.28396237552505965,0.05007022831113708) P(0.2546934804038715,0.888221722312573) P(1,0)
CAB 64.0
BAD 10.000000000000002
BDA 4.000000000000005
BDC 45.999999999999986
CAD 74.0
CDA 49.99999999999999
ACD 55.99999999999999
ACB 18.0
BCD 37.99999999999999
"""