Vorkurs Mathematik

76 6. Lösungen
(k) Konstruktion der Winkelhalbierenden
des Winkels β
(m) Konstruktion des Inkreises
(l) Konstruktion der Winkelhalbierenden
des Winkels γ
6.3.2 Lösungen zum Abschnitt ” Trigonometrische Funktionen“
Aufgaben:
1. (a) a = 6 cm, b = 2.5 cm, c = 6.5 cm, α = 67.4 ◦ , β = 22.6 ◦ , γ = 90 ◦
(b) a = 280 m, b = 360 m, c = 456.07 m, α = 37.9 ◦ , β = 52.1 ◦ , γ = 90 ◦
(c) a = 24.8 m, b = 34.2 m, c = 42.26 m, α = 35.9 ◦ , β = 54.1 ◦ , γ = 90 ◦
(d) a = 47 m, b = 36.7 m, c = 59.6 m, α = 52 ◦ , β = 38 ◦ , γ = 90 ◦
47.1 m, b = 24.5 m, c = 53.1 m, α = 62.5 ◦ , β = 27.5 ◦ , γ = 90 ◦
138 m, c = 182.9 m, α = 41 ◦ , β = 49 ◦ , γ = 90 ◦
6.4 km, α = 32 ◦ , β = 58 ◦ , γ = 90 ◦
40.6 ◦ , β = 49.4 ◦ , γ = 90 ◦
46 ◦ , β = 44 ◦ , γ = 90 ◦
(e) a =
(f) a = 120 m, b =
(g) a = 3.4 km, b = 5.4 km, c =
(h) a = 15.8 m, b = 18.46 m, c = 24.3 m, α =
(i) a = 40.55 cm, b = 39.2 cm, c = 56.4 cm, α =
2. (a) a = 6 cm, b = 8 cm, c = 10 cm, α = 36.9 ◦ , β = 53.1 ◦ , γ = 90 ◦ , p = 3.6 cm, q =
6.4 cm, hc = 4.8 cm (b) a = 4.27 m, b = 4.5 m, c = 6.2 m, α = 43.5 ◦ , β =
46.5 ◦ , γ = 90 ◦ , p = 2.9 m, q = 3.3 m, hc = 3.1 m (c) a = 8 m, b = 15.04 m, c =
17.04 m, α = 28 ◦ , β = 62 ◦ , γ = 90 ◦ , p = 3.76 m, q = 13.3 m, hc = 7.06 m
(d) a = 11.41 cm, b = 3.71 cm, c = 12 cm, α = 72 ◦ , β = 18 ◦ , γ = 90 ◦ , p =
10.85 cm, q = 1.15 cm, hc = 3.53 cm (e) a = 9.61 m, b = 10.86 m, c = 14.5 m, α =
41.5 ◦ , β = 48.5 ◦ , γ = 90 ◦ , p = 6.37 m, q = 8.13 m, hc = 7.2 m (f) a = 14 cm, b =
25.8 cm, c = 29.35 cm, α = 28.5 ◦ , β = 61.5 ◦ , γ = 90 ◦ , p = 6.68 cm, q = 22.68 cm, hc =
12.31 cm
3. (a) a = 58.6 m, b = 58.6 m, c = 55.02 m, α = 62 ◦ , β = 62 ◦ , γ = 56 ◦ , hc =
51.74 m, Flächeninhalt = 1423.44 m 2
(b) a = 45.2 m, b = 45.2 m, c = 68.23 m, α =
41 ◦ , β = 41 ◦ , γ = 98 ◦ , hc = 29.65 m, Flächeninhalt = 1011.58 m 2
(c) a = 77.13 m, b = 77.13 m, c = 124.8 m, α = 36 ◦ , β = 36 ◦ , γ = 108 ◦ , hc =
45.34 m, Flächeninhalt = 2829 m 2
(d) a = 7.63 m, b = 7.63 m, c = 9.76 m, α =
50.25 ◦ , β = 50.25 ◦ , γ = 79.5 ◦ , hc = 5.87 m, Flächeninhalt = 28.63 m 2
Vorkurs Mathematik FB A/I H Harz