Repérage sur une sphère
L’espace - Mathématiques 3e
Exercice 1 : Calculer la longueur de l'équateur ou d'un méridien à partir du rayon/diamètre de la planète
Sur une planète de diamètre \( 6\:800\:\text{km} \), on définit l'équateur de la même manière que sur Terre.
Quelle est la longueur de l'équateur de cette planète ?
On arrondira le résultat au kilomètre près, suivi de l'unité qui convient.
On arrondira le résultat au kilomètre près, suivi de l'unité qui convient.
Exercice 2 : 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 Cam Ranh (Vietnam).
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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 Cam Ranh
Sachant que \( \widehat{ECD} = 12 ° \), \( \widehat{SCE} = 90 ° \), \( \widehat{DCN} = 78 ° \) et \( \widehat{ABD} = 109 ° \), donner la latitude de la ville de Cam Ranh (Vietnam).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exercice 3 : 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 de Xochimilco (Mexique).
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"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": 6.527036446661392, "y": 13.680805733026748, "z": -37.01666313593294}, "point_render": {"color": 16711680, "size": 128}, "label_render": {"color": 16711680}}, "Label_for_Point3D_D": {"type": "Label", "position": {"x": 6.527036446661392, "y": 13.680805733026748, "z": -37.01666313593294}, "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 de Xochimilco
Donner les coordonnées géographique de la ville de Xochimilco (Mexique).
Par exemple:
Par exemple:
- Pour la ville de Columbia (États-Unis) on donnera une réponse de la forme \(\left(39° N; 92° O\right)\)
- Pour la ville de Voronej (Russie) on donnera une réponse de la forme \(\left(52° N; 39° E\right)\)
Exercice 4 : Lire les coordonnées géographiques d'une ville sur terre à partir des angles
Sur le schéma ci-dessous, le point D symbolise la ville de Honolulu (États-Unis).
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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 Honolulu
Sachant que \( \widehat{ABD} = 158 ° \), \( \widehat{ECD} = 21 ° \), \( \widehat{DCN} = 69 ° \) et \( \widehat{SCE} = 90 ° \), donner les coordonnées géographique de la ville de Honolulu (États-Unis).
Par exemple:
Par exemple:
- Pour la ville de Cibinong (Indonésie) on donnera une réponse de la forme \(\left(6° S; 107° E\right)\)
- Pour la ville d'Alcalá de Henares (Espagne) on donnera une réponse de la forme \(\left(40° N; 3° O\right)\)
Exercice 5 : Lire latitude ou longitude d'une ville sur terre à partir des parallèles et méridiens
Sur le schéma ci-dessous, le point D symbolise la ville de Padang (Indonésie).
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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 de Padang
Donner la latitude de la ville de Padang (Indonésie).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)
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Nos exercices sont conformes aux programmes de l'Éducation Nationale de la 6e à la Terminale. Grâce à Kwyk, les élèves s'entraînent sur du calcul mental, des exercices d'arithmétique et de géométrie, des problèmes et des exercices d'application, des exercices d'algorithmique et de python, des annales du brevet des collèges et du baccalauréat. Nos exercices sont proposés sous forme de réponse libre et/ou de QCM.
Afin d'assurer un entraînement efficace et pertinent aux élèves, chaque exercice est généré avec des valeurs aléatoires. Les élèves peuvent s'entraîner grâce aux devoirs donnés sur Kwyk par leurs professeurs et aux devoirs générés par notre outil utilisant l'IA mais aussi grâce aux différents modules de travail en autonomie mis à disposition sur leur espace personnel. Pour les niveaux du collège, les élèves ont également accès à des cours constitués d'une partie théorique et d'une partie pratique.
Avec Kwyk, vous mettez toutes les chances du côté des élèves pour que les différents théorèmes, propriétés et définitions n'aient plus aucun secret pour eux.
En 2024, plus de 40 000 000 d'exercices ont été réalisés sur Kwyk en Mathématiques.
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