W

R

C

Z

\colorbox{orange}{Calcul\ de\ la\ longueur\ manquante\
d'un\ côté\ dans\ un\ triangle\ rectangle}

A

Voir/cacher la rédaction

Nouvel exercice

Si le triangle n'apparaît pas entièrement,
il est possible de déplacer le point rose.

?

?

b = Random(1, 10)
β: Random[0, 180]°
a = Random(1, 10)
S = (-7.2, 1.9)
A: S + (a, 0)
k = Circle(S, b)
B = Rotate(A, β, S)
f = Segment(S, B)
g = OrthogonalLine(S, f)
c = Random(a + 1, 15)
F = Intersect(k, g, 2)
h = Segment(F, S)
i = Segment(F, B)
texte1 = Name(S)
texte2 = Name(B)
texte3 = Name(F)
p = Circle(B, c)
L = If(a ≟ 0, B + (0, c), Intersect[p, g, 2])
j = Segment(S, L)
l = Segment(L, B)
texte6 = Name(L)
type = Random(0, 1)
Alphabet: {"A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z"}
np1 = RandomElement(Alphabet)
d = IndexOf(np1, Alphabet)
l1: {np1}
l2: Alphabet \ l1
np2 = RandomElement(l2)
l3: {np2}
l4: l2 \ l3
np3 = RandomElement(l4)
l5: {np3}
l6: l4 \ l5
np4 = RandomElement(l6)
l7: {np4}
correction = false
α = Angle(F, S, B)
γ = Angle(L, S, B)
C = Midpoint(F, B)
D = Midpoint(j)
texte5: "Le\ triangle\ " + (LaTeX[np1]) + "" + (LaTeX[np2]) + "" + (LaTeX[np4]) + "\ est\ rectangle\ en\ " + (LaTeX[np1]) + " \ 
et\ d'hypoténuse\ le\ segment\ [" + (LaTeX[np2]) + "" + (LaTeX[np4]) + "],\\
on\ peut\ donc\ appliquer\ le\ théorème\ de\ Pythagore\ :\\" + (LaTeX[np2]) + "" + (LaTeX[np4]) + "²\ =\ " + (LaTeX[np2]) + "" + (LaTeX[np1]) + "²\ +\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\\" + (LaTeX[c]) + "²\ =\ " + (LaTeX[a]) + "²\ +\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\\" + (LaTeX[c^(2)]) + "\ =\ " + (LaTeX[a^(2)]) + "\ +\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\\
donc\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\ =\ " + (LaTeX[c^(2)]) + "\ -\ " + (LaTeX[a^(2)]) + " \\" + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\ =\ " + (LaTeX[c^(2) - a^(2)]) + "\\
donc\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "\ =\ \sqrt{" + (LaTeX[c^(2) - a^(2)]) + " }\\" + (LaTeX[np1]) + "" + (LaTeX[np4]) + "  \ ≈\  " + (LaTeX[sqrt(c^(2) - a^(2))]) + ""
texte8: "Le\ triangle\ " + (LaTeX[np1]) + "" + (LaTeX[np2]) + "" + (LaTeX[np4]) + "   \ est\ rectangle\ en\ " + (LaTeX[np1]) + "  \ 
et\ d'hypoténuse\ le\ segment\ [" + (LaTeX[np2]) + "" + (LaTeX[np4]) + "],\\
on\ peut\ donc\ appliquer\ le\ théorème\ de\ Pythagore\ :\\" + (LaTeX[np2]) + "" + (LaTeX[np4]) + "²\ =\ " + (LaTeX[np2]) + "" + (LaTeX[np1]) + "²\ +\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\\" + (LaTeX[c]) + "²\ =\ " + (LaTeX[a]) + "²\ +\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\\" + (LaTeX[c^(2)]) + "\ =\ " + (LaTeX[a^(2)]) + "\ +\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\\
donc\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "²\ =\ " + (LaTeX[c^(2)]) + "\ -\ " + (LaTeX[a^(2)]) + " \\" + (LaTeX[np1]) + "" + (LaTeX[np4]) + "  ²\ =\ " + (LaTeX[c^(2) - a^(2)]) + "\\
donc\ " + (LaTeX[np1]) + "" + (LaTeX[np4]) + "\ =\ \sqrt{" + (LaTeX[c^(2) - a^(2)]) + "}\\" + (LaTeX[np1]) + "" + (LaTeX[np4]) + " \ =\  " + (LaTeX[sqrt(c^(2) - a^(2))]) + " "
texte9: "Le\ triangle\ " + (LaTeX[np1]) + "" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "\ est\ rectangle\ en\ " + (LaTeX[np1]) + "\ 
et\ d'hypoténuse\ le\ segment\ [" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "],\\
on\ peut\ donc\ appliquer\ le\ théorème\ de\ Pythagore\ :\\" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "²\ =\ " + (LaTeX[np2]) + "" + (LaTeX[np1]) + "²\ +\ " + (LaTeX[np1]) + "" + (LaTeX[np3]) + "²\\" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "²\ =\ " + (LaTeX[a]) + "²\ +\ " + (LaTeX[b]) + "²\\" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "²\ =\ " + (LaTeX[a^(2)]) + "\ +\ " + (LaTeX[b^(2)]) + "\\" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "²\ =\ " + (LaTeX[a^(2) + b^(2)]) + "\\
donc\ " + (LaTeX[np2]) + "" + (LaTeX[np3]) + "\ =\ \sqrt{" + (LaTeX[a^(2) + b^(2)]) + "}\\" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "\ =\  " + (LaTeX[sqrt(a^(2) + b^(2))]) + ""
texte13: "Le\ triangle\ " + (LaTeX[np1]) + "" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "   \ est\ rectangle\ en\ " + (LaTeX[np1]) + " \ 
et\ d'hypoténuse\ le\ segment\ [" + (LaTeX[np2]) + "" + (LaTeX[np3]) + "  ],\\
on\ peut\ donc\ appliquer\ le\ théorème\ de\ Pythagore\ :\\  " + (LaTeX[np2]) + "" + (LaTeX[np3]) + "²\ =\  " + (LaTeX[np2]) + "" + (LaTeX[np1]) + " ²\ +\ " + (LaTeX[np1]) + " " + (LaTeX[np3]) + " ²\\  " + (LaTeX[np2]) + "" + (LaTeX[np3]) + "²\ =\  " + (LaTeX[a]) + "²\ +\  " + (LaTeX[b]) + "²\\ " + (LaTeX[np2]) + " " + (LaTeX[np3]) + "²\ =\ " + (LaTeX[a^(2)]) + " \ +\ " + (LaTeX[b^(2)]) + " \\  " + (LaTeX[np2]) + "" + (LaTeX[np3]) + "²\ =\ " + (LaTeX[a^(2) + b^(2)]) + " \\
donc\  " + (LaTeX[np2]) + " " + (LaTeX[np3]) + "\ =\ \sqrt{" + (LaTeX[a^(2) + b^(2)]) + " }\\ " + (LaTeX[np2]) + "" + (LaTeX[np3]) + " \ ≈\  " + (LaTeX[sqrt(a^(2) + b^(2))]) + " "
E = (-16.7, 9)
G = (-12.96025432977077, 9)
depart: false
H = (-16.6, 9)
I = (-12.860254329770774, 9)