1

2

3

4

a=

b=

c=

B=

C=

Dos ángulos y un lado

Aleja

Acerca

c

b

A=

Dos lados y el ángulo comprendido

a,b,C

A

c

Los tres lados

A

A

A_2

A_1

No\: existe\: solución. 

Dos lados y ángulo no comprendido.

1

Dos ángulos y un lado

Dos lados y el ángulo comprendido

Dos lados y ángulo no comprendido

Los tres lados

2

3

4

Resolver triángulo

No se forma triángulo

Solución única

A

A

\frac{a}{sen\:\hat{A}}=\frac{c}{sen\:\hat{C}};

a = 7 (slider from 1 to 10, step 1)
b = 5 (slider from 0 to 10, step 1)
c = 10 (slider from 0 to 10, step 1)
angA = 66 (slider from 0 to 178.9, step 1)
CasillaDeEntrada1 = Textfield(a)
angB = 30 (slider from 1 to 178, step 1)
angC = 110 (slider from 1 to 179 - angB, step 1)
CasillaDeEntrada3 = Textfield(b)
CasillaDeEntrada4 = Textfield(c)
CasillaDeEntrada5 = Textfield(angB)
CasillaDeEntrada6 = Textfield(angC)
caso: 1
C: (0, 0)
d = Circle(C, a)
f = Line(C, xAxis)
B = Intersect(d, f, 2)
f' = Rotate(f, angC°, C)
f'_1 = Rotate(f, (-(angB°)), B)
A = Intersect(f', f'_1)
ladoa = Segment(C, B)
α = Angle(B, C, A)
β = Angle(C, B, A)
b1 = Segment(C, A)
h = Segment(B, A)
polígono1, a_1, b_1, c_1 = Polygon(C, B, A)
angA1: 180 - angB - angC
texto11: "\hat{A}=180°-\hat{B}-\hat{C}=" + (LaTeX[angA1]) + "°"
CasillaDeEntrada2 = Textfield(angA)
b1_1: (a * sin(angB°) / sin(angA1°))
texto4: "
=\frac{" + (LaTeX[a]) + "·sen " + (LaTeX[angB]) + "°}{sen\:" + (LaTeX[angA1]) + "°}=" + (LaTeX[b1_1]) + ""
texto11a: "\frac{b}{sen\:\hat{B}}=\frac{a}{sen \:\hat{A}}⇒b=\frac{a\:sen\hat{B}}{sen\:\hat{A}}" + (LaTeX[texto4]) + ""
c1: (a * sin(angC°) / sin(angA1°))
texto11c: "\frac{c}{sen\:\hat{C}}=\frac{a}{sen \:\hat{A}}⇒c=\frac{a\:sen\hat{C}}{sen\:\hat{A}} =\frac{" + (LaTeX[a]) + "sen" + (LaTeX[angC]) + "°}{sen" + (LaTeX[angA1]) + "°}=" + (LaTeX[c1]) + ""
sr2 = Ray(C, B)
B' = Rotate(C, angC°, C)
C' = Rotate(B, angC°, C)
sr2' = Ray(B', C')
k = Circle(C, b)
A2 = Intersect(k, sr2')
i = Segment(C, A2)
j = Segment(B, A2)
γ = Angle(B, C, A2)
polígono2, d_1, c_2, b_2 = Polygon(B, C, A2)
c2: sqrt(a^(2) + b^(2) - (((2 * a) * b) * cos(angC°)))
texto21a: "c=\sqrt{a^2+b^2-2ab\:cos\hat{C}}=\sqrt{" + (LaTeX[a]) + "^2+" + (LaTeX[b]) + "^2-2·" + (LaTeX[a]) + "·" + (LaTeX[b]) + "·cos" + (LaTeX[angC]) + "°}=" + (LaTeX[c2]) + ""
angA2: (acos((b^(2) + c2^(2) - a^(2)) / (((2 * b) * c2))) * 180 / π)
δ = Angle(C, A2, B)
angB2: 180 - angC - angA2
texto21c: "\hat{B}=180°-\hat{A}-\hat{C}=180°-" + (LaTeX[angA2]) + "°-" + (LaTeX[angC]) + "°=" + (LaTeX[angB2]) + "°"
ε = Angle(A2, B, C)
e = Circle(B, c)
E = Intersect(k, e, 1)
l = Segment(C, E)
m = Segment(B, E)
lista2 = Sort({a, b, c})
triok: Element[lista2, 1] + Element[lista2, 2] > Element[lista2, 3]
angA4: (acos((b^(2) + c^(2) - a^(2)) / (((2 * b) * c))) * 180 / π)
cosangA4: (b^(2) + c^(2) - a^(2)) / (((2 * b) * c))
texto13_1: "cos\:\hat{A}=\frac{b^2+c^2-a^2}{2 \:b\:c}=" + (LaTeX[cosangA4]) + ""
texto14_1: "\hat{A}=arcos(" + (LaTeX[cosangA4]) + ")=" + (LaTeX[angA4]) + "°"
cosangB4: (a^(2) + c^(2) - b^(2)) / (((2 * a) * c))
angB4: (acos(cosangB4) * 180 / π)
texto15: "cos\:\hat{B}=\frac{a^2+c^2-b^2}{2\:a\:c}=" + (LaTeX[cosangB4]) + ""
texto16: "\hat{B}=arcos\left(  " + (LaTeX[cosangB4]) + " \right) =" + (LaTeX[angB4]) + "°"
angC4: 180 - angA4 - angB4
texto17: "\hat{C}=180°-\hat{A}-\hat{B}=180°-" + (LaTeX[angA4]) + "°-" + (LaTeX[angB4]) + "°=" + (LaTeX[angC4]) + "°"
ζ = Angle(E, C, B)
cir4 = Circle(C, b)
F = Point(cir4)
n = Segment(C, F)
q = Ray(B, C)
C'_1 = Rotate(B, angB°, B)
B'_1 = Rotate(C, ((-angB))°, B)
sr4 = Ray(C'_1, B'_1)
η = Angle(B'_1, B, C)
texto12a: "a=" + a + ""
G, H = Intersect(cir4, sr4)
r = Segment(C, H)
s = Segment(C, G)
o: (a * sin(angB°) / b)
t: (asin(o) * 180 / π)
θ = Angle(C, H, B)
ι = Angle(C, G, B)
lista1: {H, G}
lista3 = RemoveUndefined(lista1)
nsol3 = Length(lista3)
texto19: "\frac{a}{sen\:\hat{A}}=\frac{b}{sen\:\hat{B}}⇒sen\:\hat{A}=\frac{a\:sen\:\hat{B}}{b}=" + (LaTeX[o]) + "⇒"
texto22: "\hat{A_1}=" + (LaTeX[θ]) + ",\:\hat{A_2}=" + (LaTeX[ι]) + ""
texto23: "\hat{A}=" + (LaTeX[θ]) + ""
p1 = false
t1: a ≟ 0 ∨ angB ≟ 0 ∨ angC ≟ 0 ∨ angB + angC ≥ 180
texto10 = If(t1 ≟ true, texto14a, texto14b)
I = (-4.03305785123967, 1.3818181818181816)
J = (-1.6330578512396703, 1.3818181818181816)
K = (-1.6330578512396703, 0.5818181818181817)
L = (-4.03305785123967, 0.5818181818181817)
polígono3, l_1, i_1, j_1, k_1 = Polygon(L, I, J, K)
κ = Angle(C, A, B)
texto13c: "\hat{A}=" + (LaTeX[κ]) + ""
M = (0, 2.4)
N: M + (0, -0.85)
u = Vector(M, N)
L' = Translate(L, u)
I' = Translate(I, u)
J' = Translate(J, u)
K' = Translate(K, u)
polígono3', l', i', j', k' = Polygon(L', I', J', K')
L'' = Translate(L', u)
I'' = Translate(I', u)
J'' = Translate(J', u)
K'' = Translate(K', u)
polígono3'', l'', i'', j'', k'' = Polygon(L'', I'', J'', K'')
O = (-1.6, 2)
P = (1.2, 2)
v = Vector(O, P)
L'_1 = Translate(L, v)
I'_1 = Translate(I, v)
J'_1 = Translate(J, v)
K'_1 = Translate(K, v)
polígono3'_1, l'_1, i'_1, j'_1, k'_1 = Polygon(L'_1, I'_1, J'_1, K'_1)
L''_1 = Translate(L', v)
I''_1 = Translate(I', v)
J''_1 = Translate(J', v)
K''_1 = Translate(K', v)
polígono3''_1, l''_1, i''_1, j''_1, k''_1 = Polygon(L''_1, I''_1, J''_1, K''_1)
L''' = Translate(L'', v)
I''' = Translate(I'', v)
J''' = Translate(J'', v)
K''' = Translate(K'', v)
polígono3''', l''', i''', j''', k''' = Polygon(L''', I''', J''', K''')
texto21b: "cos\:\hat{A}=\frac{b^2+c^2-a^2}{2\:b\:c}⇒\hat{A}=arcos\left(\frac{b^2+c^2-a^2}{2\:b\:c}   \right) =" + (LaTeX[δ]) + ""
texto1: "b=" + b + ""
texto13a_1: "\hat{C}=" + (LaTeX[α]) + ""
texto13b: "\hat{B}=" + (LaTeX[β]) + ""
texto12b_1: "c=" + h + ""
texto12c: "b=" + (LaTeX[b1]) + ""
texto22a: "\hat{B}=" + (LaTeX[ε]) + ""
texto3: "\hat{A}=" + (LaTeX[δ]) + ""
texto2: "\hat{C}=" + (LaTeX[γ]) + ""
D = Point(m)
polígono4, d_2, c_3, e_1 = Polygon(C, E, D)
texto5: "b=" + b + ""
texto6: "c=" + c + ""
λ = Angle(C, E, B)
μ = Angle(E, B, C)
ν = Angle(B, C, E)
texto8: "\hat{A}=" + (LaTeX[λ]) + ""
texto9: "\hat{B}=" + (LaTeX[μ]) + ""
texto12: "\hat{C}=" + (LaTeX[ν]) + ""
texto13: "c=" + b_2 + ""
polígono5, g, c_4, b_3 = Polygon(C, B, G)
polígono6, h_1, c_5, b_4 = Polygon(C, B, H)
texto14: "c=" + h + ""
texto18: "b=" + c_1 + ""
texto24: "A=" + κ + ""
texto25: "c=" + c2 + ""
texto26: "A=" + δ + ""
texto27: "B=" + ε + ""
Q = Point(e)
p = Segment(B, Q)
R = Point(k)
f_1 = Segment(C, R)
l1 = Element(lista2, 1)
l2 = Element(lista2, 2)
l3 = Element(lista2, 3)
texto12_1: "No se forma triángulo. " + l1 + "+" + l2 + "≤" + l3 + ""
texto28: "A=" + λ + ""
texto29: "B=" + μ + ""
texto30: "C=" + ν + ""
texto31: "\hat{B}=" + (LaTeX[η]) + ""
nsol = If(a ≠ b, nsol3, 1)
ξ = Angle(H, C, B)
texto32: "\hat{C_1}=180°-" + (LaTeX[angB]) + "°-" + (LaTeX[θ]) + "=" + (LaTeX[ξ]) + ""
ο = Angle(G, C, B)
texto33: "\hat{C_2}=180°-" + (LaTeX[angB]) + " °-" + (LaTeX[ι]) + " =" + (LaTeX[ο]) + ""
texto34: "\hat{C}=180°-" + (LaTeX[angB]) + "°-" + (LaTeX[θ]) + "=" + (LaTeX[ξ]) + ""
texto35: "\hat{A}=" + (LaTeX[θ]) + ""
w: (a * sin(ξ) / sin(θ))
texto36: "\frac{a}{sen\:\hat{A}}=\frac{c}{sen\:\hat{C}};c=\frac{" + (LaTeX[a]) + "·sen" + (LaTeX[ξ]) + "}{sen" + (LaTeX[θ]) + "}=" + (LaTeX[w]) + ""
texto20: "Número de soluciones = " + nsol + ""
g_1 = Distance(H, B)
n_1 = Distance(G, B)
m_1 = Distance(H, B)
texto38: "c_1=" + (LaTeX[m_1]) + ";c_2=" + (LaTeX[n_1]) + ""
texto39: "\hat{A_1}=" + (LaTeX[θ]) + ""
texto40: "\hat{A_2}=" + (LaTeX[ι]) + ""
texto41: "\hat{C_1}=" + (LaTeX[ξ]) + ""
texto42: "\hat{C_2}=" + (LaTeX[ο]) + ""
texto43: "b=" + b + ""
p_1 = CircleArc(C, G, H)
texto44: "\hat{A_1}=" + (LaTeX[θ]) + ";\hat{A_2}=" + (LaTeX[ι]) + ""
texto45: "\hat{C_1}=" + (LaTeX[ξ]) + ";\hat{C_2}=" + (LaTeX[ο]) + ""
texto46: "c_1=" + (LaTeX[m_1]) + ";c_2=" + (LaTeX[n_1]) + ""
texto47: "\hat{A}=" + (LaTeX[θ]) + ""
texto48: "\hat{C}=" + (LaTeX[ξ]) + ""
texto49: "c=" + (LaTeX[m_1]) + ""
texto50: "A=" + (LaTeX[θ]) + ""
texto51: "C=" + (LaTeX[ξ]) + ""
texto52: "c=" + (LaTeX[m_1]) + ""