Author: José A. Mora

Experimenta

Experimenta

Ejercicios

Nuevo ejercicio

\frac{ED}{GH}=\frac{DI}{GI}

Los \;  triángulos \;  semejantes \;  son \;  EDI  \; y  \; HGI

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Solución

ED = x

Altura del edificio  x   m

Ejercicios

Para calcular la altura debes hacer coincidir
los puntos E (cornisa del edificio) y T (visual
del edificio que se refleja en el espejo en I)

Avanza o retrocede el observador con G o bien
acerca o aleja el espejo a la persona con los 
botones de la ventana izquierda.

B = (25.892126228978242, -10.049601649413376)
A4: Random[150, 250] / 10
h: A4
A = (-4.107873771021756, -10.049601649413376)
a = Line(A, B)
D = Point(a)
u = 1.9500000000000044 (slider from 1 to 5, step 0.05)
G = Point(a)
l1 = 1.5 (slider from 1.4 to 1.9, step 0.05)
A5: Random[15, 25] / 8
p1 = 1 (slider from 0 to 1, step 1)
l: l1
G1: G + (0, l)
h1 = 20 (slider from 12 to 28, step 0.5)
A3 = Random(20, 50)
B3: (A3 * π / 180)
M = (-4.54, -0.02)
L = (-4.54, 1.98)
O1 = Rotate(M, B3, L)
p = Circle(L, M)
N = Point(p)
q = CircleArc(L, M, N)
O2 = Point(q)
g = OrthogonalLine(G, a)
H: G1
O = If(p1 ≟ 0, O2, O1)
t = Segment(L, O)
i_1 = Line(H, t)
Q = Intersect(i_1, a)
b = OrthogonalLine(D, a)
D1: D + (0, h)
E: D1
f_1 = Line(E, t)
P = Intersect(a, f_1)
C = Point(a)
c = OrthogonalLine(C, a)
d = OrthogonalLine(E, b)
F = Intersect(c, d)
polígono1, f, c_1, d_1, e = Polygon(F, C, D, E)
K = Point(a)
j = Segment(E, K)
α = Angle(E, K, D)
distanciaED = Distance(E, D)
TextoED: Name[E] + (Name[D]) + " \, = \, " + distanciaED
distanciaGH = Distance(G, H)
TextoGH: Name[G] + (Name[H]) + " \, = \, " + distanciaGH
S: G - (u, 0)
I: S
distanciaGI = Distance(G, I)
TextoGI: Name[G] + (Name[I]) + " \, = \, " + distanciaGI
polígono2, h_1, g_1, i = Polygon(G, I, H)
J: S
k = Line(E, g_1)
distanciaJD = Distance(J, D)
TextoJD: Name[J] + (Name[D]) + " \, = \, " + distanciaJD
m = Segment(L, M)
n = Segment(L, N)
r = Segment(M, L)
s = CircleArc(L, M, O)
polígono4, l_1, m_1, o = Polygon(M, O, L)
R = Intersect(q, s, 1)
β = Angle(M, L, O)
n2 = 0 (slider from 0 to 4, step 1)
texto6: "\frac{x}{" + (LaTeX[distanciaGH]) + "}=\frac{" + (LaTeX[distanciaJD]) + "}{" + (LaTeX[distanciaGI]) + "}"
texto2: "x = \frac{" + (LaTeX[distanciaGH]) + "·" + (LaTeX[distanciaJD]) + "}{" + (LaTeX[distanciaGI]) + "}= " + (LaTeX[(Distance[H, G] * Distance[D, J] / Distance[G, I])]) + ""
n1 = 0 (slider from 0 to 1, step 1)
texto7: "Paso " + n2 + ""
texto9: "Inclinación de los 
rayos solares
     " + β + ""
j_1 = Segment(H, S)
k_1 = OrthogonalLine(S, a)
H' = Mirror(H, k_1)
n_1 = Ray(S, H')
T = Intersect(n_1, b)
polígono3, s_1, t_1, d_2 = Polygon(T, D, S)
texto5: "Altura de la persona " + l1 + "  m"
U = Intersect(s_1, t_1)
dd: abs(y(T) - y(E))
p_1 = Ray(D, E)
texto11: "Distancia de la persona 
     al espejo " + u + " m"