from random import random
import math
import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline


def acute(a, b, c):
    cosa = (a**2 - b**2 + c**2)/(2 * a * c)
    cosb = (b**2 - a**2 + c**2)/(2 * b * c)
    cosc = (b**2 - c**2 + a**2)/(2 * b * a)
    if cosa > 1 or cosa < -1 or cosb > 1 or cosb < -1 or cosc > 1 or cosc < -1:
        return False
    if (math.acos(cosa) < 1.5708) and (math.acos(cosb) < 1.5708) and (math.acos(cosc) < 1.5708):
        return True
    else:
        return False

def triangle(N):
    n = 0
    for i in range(N):
        x = random()
        y = random()
        if x < y:
            a = x
            b = y - x
            c = 1 - y
        else:
            a = y
            b = x - y
            c = 1 - x
        # Condition:
        if b < a > c:
            if (a < b + c) and acute(a, b, c):
                n += 1
        elif (a < b > c) and acute(a, b, c):
            if b < a + c:
                n += 1
        else:
            if (c < a + c) and acute(a, b, c):
                n += 1
    return n/N
N = 10000
print("Answer:")
print(triangle(N))

x = [i for i in range(1, 10000, 100)]
y1 = []

for i in range(1, 1000, 10):
    y1.append(A(i))


plt.plot(x[2:], y1[2:])
plt.title('PLOT')
plt.show()