Pour aller plus loin (Ancien programme) - 5e

Géométrie dans l'espace

Exercice 1 : Lire latitude ou longitude d'une ville sur terre à partir des angles

Sur le schéma ci-dessous, le point D symbolise la ville de Novotroïtsk (Russie).

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On pourra faire pivoter la figure en cliquant dessus.

Légende

Méridien d'origine Greenwich 0°
Méridien du point D
Équateur 0°
Parallèle du point D
N : Pôle nord
S : Pôle sud
C : Centre de la terre
D : Ville de Novotroïtsk

Sachant que \( \widehat{ECD} = 51 ° \), \( \widehat{ABD} = 58 ° \), \( \widehat{SCE} = 90 ° \) et \( \widehat{DCN} = 39 ° \), donner la longitude de la ville de Novotroïtsk (Russie).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)

Exercice 2 : Lire les coordonnées d'un point dans un plan 3D

Dans le repère ci-dessous, donner les coordonnées du point M sous la forme \((x ; y ; z)\).

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Exercice 3 : Calcul de l'aire d'une sphère

Soit une sphère de \( 11 cm \) de rayon.

Calculer son aire.
On donnera un résultat exact.

Exercice 4 : Calculer le rayon d'un parallèle

On assimile la Terre à une sphère de rayon \( 6\:400\:\text{km} \).

On pourra faire pivoter la figure en cliquant dessus.

Légende

Équateur 0°
Parallèle passant par D
N : Pôle nord
S : Pôle sud
D : Ville de Moratuwa

Déterminer le rayon du parallèle passant à Moratuwa de coordonnées (7° N, 80° E).
On arrondira donnera un résultat arrondi au \( km \).

Exercice 5 : Lire les coordonnées géographique d'une ville sur terre à partir des parallèles et méridiens

Sur le schéma ci-dessous, le point D symbolise la ville d'Ourguentch (Ouzbékistan).

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6.28318530718, "radius": {"x": 20.500000000000004, "y": 20.500000000000004}}}]}, "PlaneSurface_51": {"position": {"x": 0.0, "y": 34.64101615137754, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 0.0, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 8487415, "linewidth": 4}, "surface_render": {"visible": false}, "type": "PlaneSurface", "path": "Circle_50"}, "Circle_50": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 20.500000000000004, "y": 20.500000000000004}}}]}, "PlaneSurface_53": {"position": {"x": 0.0, "y": -39.39231012048832, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 0.0, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 8487415, "linewidth": 4}, "surface_render": {"visible": false}, "type": "PlaneSurface", "path": "Circle_52"}, "Circle_52": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 7.445927106677217, "y": 7.445927106677217}}}]}, "PlaneSurface_55": {"position": {"x": 0.0, "y": 39.39231012048832, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 0.0, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 8487415, "linewidth": 4}, "surface_render": {"visible": false}, "type": "PlaneSurface", "path": "Circle_54"}, "Circle_54": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 7.445927106677217, "y": 7.445927106677217}}}]}, "Point3D_D": {"type": "Point", "position": {"x": -15.320888862379563, "y": 25.71150438746157, "z": 26.53655792675753}, "point_render": {"color": 16711680, "size": 128}, "label_render": {"color": 16711680}}, "Label_for_Point3D_D": {"type": "Label", "position": {"x": -15.320888862379563, "y": 25.71150438746157, "z": 26.53655792675753}, "text": "D", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 16711680}}}}

On pourra faire pivoter la figure en cliquant dessus.

Légende

Méridien d'origine Greenwich 0°
Méridiens (espacés de 20°)
Équateur 0°
Parallèles (espacés de 20°)
N : Pôle nord
S : Pôle sud
D : Ville d'Ourguentch

Donner les coordonnées géographique de la ville d'Ourguentch (Ouzbékistan).
Par exemple:

Pour la ville de Plymouth (Royaume-Uni) on donnera une réponse de la forme \(\left(50° N; 4° O\right)\)

Pour la ville de Laventille (Trinidad et Tobago) on donnera une réponse de la forme \(\left(11° N; 61° O\right)\)

Revenir au choix du niveau