B

\text{V pravidelnom 3-bokom hranole }ABCDEF \text{ určite uhol priamok }\overleftrightarrow{AC},\overleftrightarrow{BF}.

\text{Postup

1.  \; \text{Priamky }\overleftrightarrow{AC},\overleftrightarrow{BF}

2. \; \text{Rovnobežku } r∥AC:F∈r

3. \; \text{Rovina }ρ=r∪\overleftrightarrow{BF} \text{ a uhol }α=∡DFB

4. \; \text{Zostrojme skutočnú veľkosť }\triangle BDF

=

5. \; \text{Musíme vypočítať veľkosti: }BD,DF,FB\text{ \red {alebo}

6. \; \text{Aktivujeme “Ukáž ρ v 2D pohľade” - \red{pravý klik na ρ }

A = (0, -1, 0)
r = OrthogonalLine(A, xOyPlane)
e = Circle(A, 1, r)
I = Point(e)
N = 3 (slider from 3 to 6, step 1)
B: I
mnohouholník1, d_{3}, g, i, j, k, l, C, D_{1}, E_{1}, F_{1} = Polygon(A, B, N, xOyPlane)
text3: "\pmb " + (LaTeX[N]) + " \text{ - uholník pravidelný: } A" + (LaTeX[A]) + ",B" + (LaTeX[B]) + ", C(?,?,0), ...∈ π  "
h = Line(A, xAxis)
p = OrthogonalLine(A, xOyPlane)
koef = 1 (slider from 0.2 to 1.5, step 0.1)
d = Circle(A, (koef * Distance[A, B]), h)
tv = SurdText(koef)
G = (6, -4)
a, D, E, F, K, L, M, stenaABIH, stenaBCJI, stenaCDKJ, stenaDELK, stenaEFML, stenaAFMH, stenaHIJKLM, hranaAH, hranaBI, hranaCJ, hranaDK, hranaEL, hranaFM, hranaHI, hranaIJ, hranaJK, hranaKL, hranaLM, hranaHM = Prism(mnohouholník1, (koef * Distance[A, B]))
vzdialenosťAH = Distance(A, D)
vzdialenosťAB = Distance(A, B)
text5: "\text{ Hranol }ABCDEF:\left|AD  \right| =" + (LaTeX[tv]) + "\left| AB \right| "
text4: "koef=" + (LaTeX[tv]) + ""
c = Circle(hranaAH, A)
m = Line(A, C)
n = Line(B, F)
q = Line(F, m)
ρ = Plane(D, F, B)
α = Angle(D, F, B)
t1, d_r, d_z, d_{1} = Polygon(B, D, F)
text12: "\text{Uhol }α=" + (LaTeX[α]) + ""
text13 = SurdText(d_z)
text14: "" + (LaTeX[text13]) + ""
text15 = SurdText(d_r)
text16: "" + (LaTeX[text15]) + ""
f = OrthogonalLine(B, q, ρ)
H = Intersect(q, f)
text18 = SurdText(Distance[B, H])
text19 = SurdText(Distance[D, F] / 2)
text20: "\left|BH  \right| =" + (LaTeX[text18]) + ";\left| FH \right| =" + (LaTeX[text19]) + ""
text21 = SurdText(Distance[B, H] / Distance[B, D])
BH = Distance(B, H)
BD = Distance(B, D)
text17: "\text{sin}(α)=\frac{\left| BH \right| }{\left| BF \right| }=" + (LaTeX[text21]) + ""
β: asind(BH / BD)
text22: "α=" + (LaTeX[β]) + ""