position

?

Triangle MPH

Triangle ABC

PH=?

Triangle MPH

Triangle ABC

PH=?

...

...

...

MP=?

HM=?

...

...

...

Triangle MPH

Triangle ABC

PH=?

HM=?

...

...

...

HM=?

...

Triangle MPH

Triangle ABC

PH=?

HM=?

BC=?

Triangle MPH

Triangle ABC

PH=?

HM=?

...

Tableau

longueurs

agrandissement

rapports

\frac{\red{MA}}\darkgreen{{MP}}=\frac{\red{MB}}\darkgreen{{MH}}=\frac\red{{AB}}\darkgreen{{PH}}

\frac{\red{MA}}\darkgreen{{MP}}=\frac{\red{...}}\darkgreen{{...}}=\frac\red{{...}}\darkgreen{{...}}

\frac{\red{MA}}\darkgreen{{MP}}=\frac{\red{MB}}\darkgreen{{MH}}=\frac\red{{...}}\darkgreen{{...}}

\frac{\red{...}}\darkgreen{{...}}=\frac{\red{...}}\darkgreen{{...}}=\frac\red{{...}}\darkgreen{{...}}

hauteur\ de\ l'arbre = ?

A

position 1/2

longueurs

B

j: y = 0
K_1 = Point(j)
M: K_1 + (1.7, 0)
g_2 = Ray(M, M + (0, -1))
s_1 = OrthogonalLine(K_1, j)
F_1 = Point(s_1)
t_1 = Ray(K_1, F_1)
A = Point(xAxis)
P = Point(xAxis)
c = Line(P, P + (1, 1))
a = 1.7 (slider from 1 to 2, step 0.1)
O: A + (0, a)
b = 10.2 (slider from 4 to 30, step 0.1)
H: P + (0, b)
l = 0.6 (slider from 0 to 1, step 0.1)
O': O + (l, 0)
L: O' + (0, (-l))
O1 = Point(Segment[L, O'])
O2: O1 + (0, l)
f = Segment(O, O')
g = Segment(O1, O2)
h = Ray(O, O2)
i = Ray(O, O1)
C_1: P + (((-b) * 330 / 598 / 2), 0)
D: C_1 + ((b * 348 / 598), 0)
α = Angle(O1, O, O2)
d = false
BH = Distance(P, H)
A': P + ((-BH), 0)
AO = Distance(A, O)
O'': A' + (0, AO)
k = Segment(O'', P)
O''': O'' + (l, 0)
m_1 = OrthogonalLine(O''', f)
E = Intersect(m_1, k)
image2' = Dilate(image2, a / 1.7, O)
F: A + (-0.82, -0.07)
G: F + (1.021, 0)
M_1 = Point(c)
M' = Mirror(M_1, P)
M'_1 = Translate(M_1, Vector[P, M])
n = Ray(M, H)
p = Ray(A, A + (0, 1))
B = Point(p)
q = Segment(B, A)
r = Line(B, n)
C = Intersect(j, r)
s = Ray(C, B)
t = Segment(C, A)
f_1 = Segment(H, P)
B_1 = Midpoint(f_1)
g_1 = Line(B, j)
K = Intersect(g_1, n)
h_1 = OrthogonalLine(K, j)
N = Intersect(h_1, j)
β = Angle(H, P, M)
γ = Angle(B, A, C)
AB = Distance(A, B)
PH = Distance(P, H)
AC = Distance(A, C)
SP = Distance(M, P)
texte4 = TableText({{A1, B1, C1, D1}, {A2, B2, C2, D2}}, "|_llll")
MP = Distance(M, P)
C4: "MP" = MP
C7: "MP" = MP
B8: "AB" = AB
C10: "MP" = MP
B11: "AB" = AB
C11: "AC" = AC
texte5 = TableText({{A4, B4, C4, D4}, {A5, B5, C5, D5}}, "|_llll")
texte8 = TableText({{A7, B7, C7, D7}, {A8, B8, C8, D8}}, "|_llll")
texte9 = TableText({{A10, B10, C10, D10}, {A11, B11, C11, D11}}, "|_llll")
I = (-10.148585208617884, -3.6935774593675577)
C13: "MP" = MP
B14: "AB" = AB
C14: "AC" = AC
texte10 = TableText({{A13, B13, C13, D13}, {A14, B14, C14, D14}}, "|_llll")
m = 6 (slider from 0 to 10, step 1)
e = false
o = true
texte2: "PH=\frac{" + (LaTeX[AB]) + "×" + (LaTeX[MP]) + "}{" + (LaTeX[AC]) + "}≈" + (LaTeX[(AB * MP / AC)]) + ""
J = Point(j)
texte11: "\frac{MP}{AC}≈\frac{" + (LaTeX[MP]) + "}{" + (LaTeX[AC]) + "}≈" + (LaTeX[MP / AC]) + ""
texte12: "PH≈" + (LaTeX[AB]) + "×" + (LaTeX[MP / AC]) + "≈" + (LaTeX[(AB * MP / AC)]) + ""
Q = (-11.40385724347843, 7.063282146652322)
R = Midpoint(q)
S = Midpoint(t)
texte13: "" + (LaTeX[AC]) + ""
texte14: "" + (LaTeX[AB]) + ""
w = false
i_1 = Ray(M, M + (0, -1))
T = Point(i_1)
U: T + (MP, 0)
u_1 = Vector(T, U)
v_1 = Vector(U, T)
V = Midpoint(T, U)
texte15: "" + (LaTeX[MP]) + ""
a_1 = 0 (slider from -5 to 5, step 0.1)
u = 0 (slider from -5 to 10, step 0.1)
j_1 = Segment(M, P)
texte16_3: "\frac{\red{" + (LaTeX[Distance[C, A]]) + "}}\darkgreen{{" + (LaTeX[MP]) + "}}=\frac{\red{MB}}\darkgreen{{MH}}=\frac\red{{" + (LaTeX[AB]) + "}}\darkgreen{{PH}}"
texte17: "\darkgreen{PH}=\frac{\red{" + (LaTeX[AB]) + "}×\darkgreen{" + (LaTeX[MP]) + "}}{\red{" + (LaTeX[Distance[C, A]]) + "}}≈" + (LaTeX[(AB * MP / Distance[A, C])]) + ""
texte19: "\frac{\red{ " + (LaTeX[Distance[C, A]]) + "}}\darkgreen{{ " + (LaTeX[MP]) + "}}=\frac\red{{" + (LaTeX[AB]) + " }}\darkgreen{{PH}}"
Z = (-11.523131207921178, -3.773037033695563)
texte20: "\frac{MP}{MA}≈\frac{" + (LaTeX[MP]) + " }{ " + (LaTeX[AC]) + "}≈ " + (LaTeX[MP / AC]) + ""
A_1 = (20.34641735728703, -8.614685589969785)
D_1 = Point(j)
G_1 = Point(g_2)
L_1: M
N_1 = Midpoint(L_1, H)
P_1 = Midpoint(N_1, L_1)
Q_1 = Midpoint(N_1, H)
l_1 = Vector(L_1, P_1)
n_1 = Vector(P_1, N_1)
p_1 = Vector(N_1, Q_1)
q_1 = Vector(Q_1, H)
k_1 = OrthogonalLine(D_1, j)
E_1 = Point(g_2)
r_1 = OrthogonalLine(E_1, k_1)
I_1 = Intersect(k_1, r_1)
w_1 = Vector(E_1, I_1)
b_1 = Vector(I_1, E_1)
e_1 = OrthogonalLine(P, j)
f_2 = OrthogonalLine(G_1, t_1)
J_1 = Intersect(e_1, f_2)
d_1 = Vector(J_1, G_1)
c_1 = Vector(G_1, J_1)
image6' = Mirror(image6, M)
v = false
o_1 = false
W = Midpoint(M, P)
H_1 = Point(j)
O_1: H_1 + (0, AB)
u_2 = Vector(H_1, O_1)
v_2 = Vector(O_1, H_1)
R_1 = Translate(D_1, Vector[A, B])