На крыше коттеджа установлен флюгер в форме прямоу...

python
A = sp.Point(0,0)
B = sp.Point(15,0)
C = sp.Point(35,10)
D = sp.Point(0,10)
P = sp.Line(A,C).intersection(sp.Line(B,D))[0]
P

Point2D(21/2, 3)

python
# Represent axis line through B and C
line_axis = sp.Line(B,C)
# distance from point P to line
dist_P = line_axis.distance(P)
# farthest distance among vertices
# compute distances
dA = line_axis.distance(A)
dD = line_axis.distance(D)
dC = 0
dB = 0
dist_max = max(float(dA), float(dD))
dist_P, dist_max

(21*sqrt(5)/10, 15.652475842498529)

python
float(dA), float(dD)


(6.708203932499369, 15.652475842498529)

python
float(dist_P/ dist_max)


0.30000000000000004

python
a,b,h = sp.symbols('a b h', positive=True)
A = sp.Point(0,0)
D = sp.Point(0,h)
B = sp.Point(a,0)
C = sp.Point(b,h)
P = sp.Line(A,C).intersection(sp.Line(B,D))[0]
P

Point2D(a*b/(a + b), a*h/(a + b))

python
import random, math
def ratio(a,b,h):
    A = sp.Point(0,0)
    B = sp.Point(a,0)
    C = sp.Point(b,h)
    D = sp.Point(0,h)
    line_axis = sp.Line(B,C)
    P = sp.Line(A,C).intersection(sp.Line(B,D))[0]
    dist_P = line_axis.distance(P)
    # choose distances of A or D whichever bigger for farthest from axis
    dist_A = line_axis.distance(A)
    dist_D = line_axis.distance(D)
    dist_max = max(dist_A, dist_D)
    return float(dist_P/dist_max)
for _ in range(5):
    a = random.uniform(1,20)
    b = random.uniform(a, a+30)
    h = random.uniform(1,15)
    print(a,b,h, ratio(a,b,h))

python
def ratio_expected(a,b):
    return a/(a+b)
for a,b,h,_ in [(11.7121,36.79,2.6,0)]:
    print(ratio_expected(a,b))

python
for _ in range(5):
    a = random.uniform(1,20)
    b = random.uniform(a+0.1,a+30)
    h = random.uniform(1,15)
    r1 = ratio(a,b,h)
    r2 = a/(a+b)
    print(abs(r1-r2) < 1e-10)