Profondeur=?

Bob a fait tomber son téléphone portable dans un trou, 
il souhaite le récupérer à l'aide d'une corde et d'un sceau 
mais il se demande de quelle longueur de corde il a besoin. 
Pouvez-vous l'aider?

Profondeur du trou

Largeur du trou

Distance entre Bob et le trou

Modélisation

\frac{HJ}{KL}=\frac{HI}{IK}

Relation de Thalès

Solution:

a = 9.4 (slider from 9 to 15, step 0.1)
C: (a, 0)
B: (x(C) + 0.48, 1.77)
b = 7.3 (slider from 7 to 9, step 0.1)
A: (b, 0)
D = (9, 0)
c = -3.4 (slider from -5 to 0, step 0.1)
E: (x(A), c)
F: (x(D), c)
g = Segment(B, E)
u = Vector(A, D)
v = Vector(D, A)
distanceAD = Distance(A, D)
distanceBE = Distance(B, E)
i: y = y(E)
w = Vector(E, A)
z = Vector(A, E)
G: (x(B), 0)
l = Vector(D, G)
m = Vector(G, D)
distanceDG = Distance(D, G)
j = Integral(-(x(i) / y(i)) * x - z(i) / y(i), -100, x(E))
k = Integral(-(x(i) / y(i)) * x - z(i) / y(i), 9, 100)
d = Segment(A, D)
H = (4.902514869574563, 4.096201499055127)
I = Point(Circle[H, d])
e = Segment(H, I)
f = OrthogonalLine(H, e)
n = Segment(A, E)
J = Point(Circle[H, n])
p = Segment(H, J)
q = Segment(E, B)
r = Line(J, I)
t = Line(H, I)
distanceHI = Distance(H, I)
TexteHI: Name[H] + (Name[I]) + " \, = \, " + distanceHI
distanceAE = Distance(A, E)
distanceHJ = Distance(H, J)
s = Segment(D, G)
K = Point(Circle[I, s])
a_1 = Segment(I, K)
distanceIK = Distance(I, K)
TexteIK: Name[I] + (Name[K]) + " \, = \, " + distanceIK
distanceGB = Distance(G, B)
b_1 = OrthogonalLine(K, a_1)
L = Point(Circle[K, 1.77])
c_1 = Segment(K, L)
d_1 = Segment(J, L)
h = Integral(0 * x + 108, -100, 100)
distanceKL = Distance(K, L)
TexteKL: Name[K] + (Name[L]) + " \, = \, " + distanceKL
M = (13.29424459225156, 1.7687213414912462)
e_1 = Line(B, M)
N = Point(e_1)
f_1 = OrthogonalLine(N, e_1)
O = Intersect(k, f_1, 1)
P = Point(f_1)
TexteDG: "" + (LaTeX["Distance"]) + " \, = \, " + (LaTeX[distanceDG]) + "m"
distanceBG = Distance(B, G)
TexteAD: "" + (LaTeX["Largeur"]) + " \, = \, " + (LaTeX[distanceAD]) + "m"
TexteBG: "" + (LaTeX["Taille"]) + " \, = \, " + (LaTeX[distanceBG]) + "m"
poly1, h_1, k_1, l_1, j_1 = Polygon(H, K, L, J)
o = false
g_1 = false
KL = Distance(K, L)
HI = Distance(H, I)
IK = Distance(I, K)
i_1 = false
texte7: "Profondeur=" + ((KL * HI) / IK) + "m"
Q = (18.77338084099589, -0.3383531494470621)
R = (19.55303664796634, -0.3804967065805999)
S = (18.794452619562662, 0.7995228931584596)