Pour aller plus loin (Ancien programme) - 4e

Solides

Exercice 1 : Calcul d'une hauteur à partir du volume d'un cylindre de révolution

Un cylindre de révolution a un volume de \( 55720 cm^{3} \) et l'aire de sa base est de \( 796 cm^{2} \).

Quelle est sa hauteur?
On donnera la réponse suivie de l'unité qui convient.

Exercice 2 : Reconnaître le patron d'un pavé droit

Soit le pavé suivant :

Parmi les figures suivantes, trouver celle ou celles étant un patron de ce pavé.

A.

{"init": {"range": [[-1.25, 24.0], [-1.0, 9.25]], "scale": [20, 20]}, "line": [[[11.0, 5.0], [20.0, 5.0], {"subtype": "segment"}], [[2.0, 5.0], [2.0, 8.0], {"subtype": "segment"}], [[20.0, 5.0], [23.0, 5.0], {"subtype": "segment"}], [[20.0, 3.0], [20.0, 5.0], {"subtype": "segment"}], [[2.0, 5.0], [11.0, 5.0], {"subtype": "segment"}], [[20.0, 3.0], [23.0, 3.0], {"subtype": "segment"}], [[0.0, 0.0], [0.0, 3.0], {"subtype": "segment"}], [[11.0, 0.0], [11.0, 3.0], {"subtype": "segment"}], [[2.0, 3.0], [11.0, 3.0], {"subtype": "segment"}], [[2.0, 3.0], [2.0, 5.0], {"subtype": "segment"}], [[0.0, 3.0], [2.0, 3.0], {"subtype": "segment"}], [[2.0, 8.0], [11.0, 8.0], {"subtype": "segment"}], [[2.0, 0.0], [2.0, 3.0], {"subtype": "segment"}], [[11.0, 3.0], [20.0, 3.0], {"subtype": "segment"}], [[11.0, 3.0], [11.0, 5.0], {"subtype": "segment"}], [[23.0, 3.0], [23.0, 5.0], {"subtype": "segment"}], [[11.0, 5.0], [11.0, 8.0], {"subtype": "segment"}], [[2.0, 0.0], [11.0, 0.0], {"subtype": "segment"}], [[0.0, 0.0], [2.0, 0.0], {"subtype": "segment"}]], "label": [[[0.0, 1.5], "3 dm", "left", {}], [[21.5, 5.0], "3 dm", "above", {}], [[2.0, 6.5], "3 dm", "left", {}], [[6.5, 8.0], "9 dm", "above", {}], [[15.5, 5.0], "9 dm", "above", {}], [[2.0, 4.0], "2 dm", "left", {}], [[1.0, 3.0], "2 dm", "above", {}]]}
B.

{"init": {"range": [[-1.25, 25.0], [-1.0, 21.25]], "scale": [20, 20]}, "line": [[[0.0, 0.0], [0.0, 9.0], {"subtype": "segment"}], [[3.0, 11.0], [12.0, 11.0], {"subtype": "segment"}], [[3.0, 11.0], [3.0, 20.0], {"subtype": "segment"}], [[3.0, 9.0], [12.0, 9.0], {"subtype": "segment"}], [[24.0, 9.0], [24.0, 11.0], {"subtype": "segment"}], [[12.0, 9.0], [15.0, 9.0], {"subtype": "segment"}], [[12.0, 9.0], [12.0, 11.0], {"subtype": "segment"}], [[0.0, 11.0], [0.0, 20.0], {"subtype": "segment"}], [[3.0, 0.0], [3.0, 9.0], {"subtype": "segment"}], [[3.0, 9.0], [3.0, 11.0], {"subtype": "segment"}], [[15.0, 11.0], [24.0, 11.0], {"subtype": "segment"}], [[0.0, 9.0], [3.0, 9.0], {"subtype": "segment"}], [[0.0, 11.0], [3.0, 11.0], {"subtype": "segment"}], [[0.0, 9.0], [0.0, 11.0], {"subtype": "segment"}], [[15.0, 9.0], [15.0, 11.0], {"subtype": "segment"}], [[0.0, 20.0], [3.0, 20.0], {"subtype": "segment"}], [[12.0, 11.0], [15.0, 11.0], {"subtype": "segment"}], [[0.0, 0.0], [3.0, 0.0], {"subtype": "segment"}], [[15.0, 9.0], [24.0, 9.0], {"subtype": "segment"}]], "label": [[[0.0, 4.5], "9 dm", "left", {}], [[0.0, 10.0], "2 dm", "left", {}], [[19.5, 11.0], "9 dm", "above", {}], [[0.0, 15.5], "9 dm", "left", {}], [[7.5, 11.0], "9 dm", "above", {}], [[13.5, 11.0], "3 dm", "above", {}], [[1.5, 20.0], "3 dm", "above", {}]]}
C.

{"init": {"range": [[-1.25, 23.0], [-1.0, 22.25]], "scale": [20, 20]}, "line": [[[11.0, 0.0], [11.0, 9.0], {"subtype": "segment"}], [[0.0, 9.0], [2.0, 9.0], {"subtype": "segment"}], [[2.0, 12.0], [11.0, 12.0], {"subtype": "segment"}], [[11.0, 21.0], [13.0, 21.0], {"subtype": "segment"}], [[11.0, 9.0], [11.0, 12.0], {"subtype": "segment"}], [[11.0, 12.0], [13.0, 12.0], {"subtype": "segment"}], [[22.0, 9.0], [22.0, 12.0], {"subtype": "segment"}], [[13.0, 0.0], [13.0, 9.0], {"subtype": "segment"}], [[11.0, 9.0], [13.0, 9.0], {"subtype": "segment"}], [[13.0, 12.0], [13.0, 21.0], {"subtype": "segment"}], [[13.0, 12.0], [22.0, 12.0], {"subtype": "segment"}], [[13.0, 9.0], [22.0, 9.0], {"subtype": "segment"}], [[2.0, 9.0], [11.0, 9.0], {"subtype": "segment"}], [[11.0, 0.0], [13.0, 0.0], {"subtype": "segment"}], [[0.0, 12.0], [2.0, 12.0], {"subtype": "segment"}], [[11.0, 12.0], [11.0, 21.0], {"subtype": "segment"}], [[0.0, 9.0], [0.0, 12.0], {"subtype": "segment"}], [[2.0, 9.0], [2.0, 12.0], {"subtype": "segment"}], [[13.0, 9.0], [13.0, 12.0], {"subtype": "segment"}]], "label": [[[0.0, 10.5], "3 dm", "left", {}], [[1.0, 12.0], "2 dm", "above", {}], [[11.0, 16.5], "9 dm", "left", {}], [[12.0, 21.0], "2 dm", "above", {}], [[17.5, 12.0], "9 dm", "above", {}], [[11.0, 4.5], "9 dm", "left", {}], [[6.5, 12.0], "9 dm", "above", {}]]}
D.

{"init": {"range": [[-1.25, 14.0], [-1.0, 15.25]], "scale": [20, 20]}, "label": [[[0.0, 10.5], "3 dm", "left", {}], [[0.0, 13.0], "2 dm", "left", {}], [[12.0, 12.0], "2 dm", "above", {}], [[9.0, 4.5], "9 dm", "left", {}], [[4.5, 14.0], "9 dm", "above", {}], [[10.0, 12.0], "2 dm", "above", {}]], "line": [[[0.0, 12.0], [9.0, 12.0], {"subtype": "segment"}], [[11.0, 9.0], [11.0, 12.0], {"subtype": "segment"}], [[9.0, 9.0], [9.0, 12.0], {"subtype": "segment"}], [[11.0, 9.0], [13.0, 9.0], {"subtype": "segment"}], [[9.0, 0.0], [11.0, 0.0], {"subtype": "segment"}], [[9.0, 0.0], [9.0, 9.0], {"subtype": "segment"}], [[0.0, 12.0], [0.0, 14.0], {"subtype": "segment"}], [[9.0, 12.0], [9.0, 14.0], {"subtype": "segment"}], [[11.0, 0.0], [11.0, 9.0], {"subtype": "segment"}], [[9.0, 12.0], [11.0, 12.0], {"subtype": "segment"}], [[11.0, 12.0], [13.0, 12.0], {"subtype": "segment"}], [[0.0, 9.0], [9.0, 9.0], {"subtype": "segment"}], [[0.0, 14.0], [9.0, 14.0], {"subtype": "segment"}], [[9.0, 9.0], [11.0, 9.0], {"subtype": "segment"}], [[0.0, 9.0], [0.0, 12.0], {"subtype": "segment"}], [[13.0, 9.0], [13.0, 12.0], {"subtype": "segment"}]]}

Exercice 3 : Calcul du volume d'un prisme droit

Soit un prisme droit de \(7 cm\) de hauteur. Ses bases sont des triangles dont l'un des côtés mesure \(5 cm\) et dont la hauteur relative à ce côté est de \(6 cm\).

Calculer son volume.
On donnera la réponse suivie de l'unité qui convient.

Exercice 4 : 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 Jaraguá do Sul (Brésil).

{"options": {"render": {"sprite_scale": 0.02, "label_fontsize": 240, "sub_curve": 64}, "size": {"width": 600, "height": 500}, "camera": {"starting_position": {"x": -534, "y": 221, "z": 76}}, "materials_options": {"surface": {"opacity": 1}, "solid_line": {"linewidth": 2}, "hidden_solid_line": {"linewidth": 2, "dashSize": 2, "gapSize": 2}}}, "data": {"Sphere_0": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 0.0, "z": 0.0, "order": "XYZ"}, "type": "SpherePortion", "radius": 40, "force_second_circle": true, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": false}, "surface_render": {"visible": true, "texture": "/static/img/earthmap1k.jpg", "bumpMap": "/static/img/earthbump1k.jpg", "bumpScale": 4, "specularMap": "/static/img/earthspec1k.jpg", "offset": {"x": 3.141592653589793}}, "phiStart": 0, "phiEnd": 5.427973973702365, "plain_uv_mapping": true, "not_draw_inner": true}, "PlaneSurface_2": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 0.0, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": false}, "surface_render": {"visible": true, "color": 16685614, "depthTest": true, "phong": true, "opacity": 1}, "type": "PlaneSurface", "path": "Arc_1"}, "Arc_1": {"type": "Path2D", "path": [{"moveTo": {"x": 0, "y": 0}}, {"lineTo": {"x": -0.49086153142880334, "y": 39.99698807356578}}, {"absArc": {"center": {"x": 0, "y": 0}, "radius": 40.0, "startAngle": 1.5585244804918115, "endAngle": 4.724660826687775}}, {"lineTo": {"x": 0, "y": 0}}]}, "PlaneSurface_4": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 2.2863813201125716, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": false}, "surface_render": {"visible": true, "color": 65280, "depthTest": true, "phong": true, "opacity": 0.2}, "type": "PlaneSurface", "path": "Arc_3"}, "Arc_3": {"type": "Path2D", "path": [{"moveTo": {"x": 0, "y": 0}}, {"lineTo": {"x": -36.16423428286679, "y": 17.092342107912593}}, {"absArc": {"center": {"x": 0, "y": 0}, "radius": 40.0, "startAngle": -1.5830681730979816, "endAngle": -0.44151375921544056}}, {"lineTo": {"x": 0, "y": 0}}]}, "PlaneSurface_6": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 2.2863813201125716, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 65280, "linewidth": 2}, "surface_render": {"visible": false}, "opened": true, "type": "PlaneSurface", "path": "Arc_5"}, "Arc_5": {"type": "Path2D", "path": [{"absArc": {"center": {"x": 0, "y": 0}, "radius": 18.666666666666668, "startAngle": -1.5707963267948966, "endAngle": -0.4537856055185257}}]}, "PlaneSurface_8": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 2.2863813201125716, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": false}, "surface_render": {"visible": true, "color": 255, "depthTest": true, "phong": true, "opacity": 0.2}, "type": "PlaneSurface", "path": "Arc_7"}, "Arc_7": {"type": "Path2D", "path": [{"moveTo": {"x": 0, "y": 0}}, {"lineTo": {"x": -39.99698807356578, "y": -0.4908615314287929}}, {"absArc": {"center": {"x": 0, "y": 0}, "radius": 40.0, "startAngle": -0.46605745182161085, "endAngle": 0.01227184630308513}}, {"lineTo": {"x": 0, "y": 0}}]}, "PlaneSurface_10": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 2.2863813201125716, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 255, "linewidth": 2}, "surface_render": {"visible": false}, "opened": true, "type": "PlaneSurface", "path": "Arc_9"}, "Arc_9": {"type": "Path2D", "path": [{"absArc": {"center": {"x": 0, "y": 0}, "radius": 31.333333333333332, "startAngle": -0.4537856055185257, "endAngle": 0}}]}, "PlaneSurface_12": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 2.2863813201125716, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": false}, "surface_render": {"visible": true, "color": 16711680, "depthTest": true, "phong": true, "opacity": 0.2}, "type": "PlaneSurface", "path": "Arc_11"}, "Arc_11": {"type": "Path2D", "path": [{"moveTo": {"x": 0, "y": 0}}, {"lineTo": {"x": 0.4908615314287905, "y": -39.99698807356578}}, {"absArc": {"center": {"x": 0, "y": 0}, "radius": 40.0, "startAngle": -0.01227184630308513, "endAngle": 1.5830681730979816}}, {"lineTo": {"x": 0, "y": 0}}]}, "PlaneSurface_14": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 2.2863813201125716, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 16711680, "linewidth": 2}, "surface_render": {"visible": false}, "opened": true, "type": "PlaneSurface", "path": "Arc_13"}, "Arc_13": {"type": "Path2D", "path": [{"absArc": {"center": {"x": 0, "y": 0}, "radius": 10.0, "startAngle": 0, "endAngle": 1.5707963267948966}}]}, "Segment3D_15": {"type": "Segment", "pt1": {"x": 0.0, "y": 0.0, "z": 0.0}, "pt2": {"x": -45.0, "y": 0.0, "z": 0.0}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 0, "linewidth": 2}}, "Segment3D_16": {"type": "Segment", "pt1": {"x": 0.0, "y": 0.0, "z": 0.0}, "pt2": {"x": -29.522656304572827, "y": 0.0, "z": -33.96193111002474}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 0, "linewidth": 2}}, "Segment3D_17": {"type": "Segment", "pt1": {"x": 0.0, "y": 0.0, "z": 0.0}, "pt2": {"x": -26.534787717486626, "y": -19.726701605508485, "z": -30.524781482512697}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 0, "linewidth": 2}}, "PlaneSurface_19": {"position": {"x": 0.0, "y": -17.534845871563096, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 3.141592653589793, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": false}, "surface_render": {"visible": true, "color": 16776960, "opacity": 0.2, "depthTest": true}, "type": "PlaneSurface", "path": "Arc_18"}, "Arc_18": {"type": "Path2D", "path": [{"moveTo": {"x": 0, "y": 0}}, {"lineTo": {"x": -35.95176185196668, "y": 2.2014105037859457e-15}}, {"absArc": {"center": {"x": 0, "y": 0}, "radius": 35.95176185196668, "startAngle": -0.8552113334772214, "endAngle": 0}}, {"lineTo": {"x": 0, "y": 0}}]}, "Segment3D_20": {"type": "Segment", "pt1": {"x": 0.0, "y": -17.534845871563096, "z": 0.0}, "pt2": {"x": -40.95176185196668, "y": -17.534845871563096, "z": 0.0}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 0, "linewidth": 2}}, "Segment3D_21": {"type": "Segment", "pt1": {"x": 0.0, "y": -17.534845871563096, "z": 0.0}, "pt2": {"x": -26.866773116051757, "y": -17.534845871563096, "z": -30.9066869966807}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 0, "linewidth": 2}}, "PlaneSurface_23": {"position": {"x": 0.0, "y": -17.534845871563096, "z": 0.0}, "rotation": {"x": 1.5707963267948966, "y": 3.141592653589793, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 16776960, "linewidth": 2}, "surface_render": {"visible": false}, "opened": true, "type": "PlaneSurface", "path": "Arc_22"}, "Arc_22": {"type": "Path2D", "path": [{"absArc": {"center": {"x": 0, "y": 0}, "radius": 17.97588092598334, "startAngle": 0, "endAngle": -0.8552113334772214}}]}, "Point3D_B": {"type": "Point", "position": {"x": 1.0736996435075964e-15, "y": -17.534845871563096, "z": 0.0}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_B": {"type": "Label", "position": {"x": 1.0736996435075964e-15, "y": -17.534845871563096, "z": 0.0}, "text": "B", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "PlaneSurface_25": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": 0.0, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 6949000, "linewidth": 4}, "surface_render": {"visible": false}, "opened": true, "type": "PlaneSurface", "path": "Arc_24"}, "Arc_24": {"type": "Path2D", "path": [{"absArc": {"center": {"x": 0, "y": 0}, "radius": 40.5, "startAngle": 1.5707963267948966, "endAngle": 4.71238898038469}}]}, "PlaneSurface_27": {"position": {"x": 0.0, "y": 0.0, "z": 0.0}, "rotation": {"x": 0.0, "y": -0.8552113334772214, "z": 0.0, "order": "XYZ"}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 11294970, "linewidth": 4}, "surface_render": {"visible": false}, "opened": true, "type": "PlaneSurface", "path": "Arc_26"}, "Arc_26": {"type": "Path2D", "path": [{"absArc": {"center": {"x": 0, "y": 0}, "radius": 40.5, "startAngle": 1.5707963267948966, "endAngle": 4.71238898038469}}]}, "Segment3D_28": {"type": "Segment", "pt1": {"x": 0.0, "y": -45.0, "z": 0.0}, "pt2": {"x": 0.0, "y": 45.0, "z": 0.0}, "point_render": {"visible": false}, "label_render": {"visible": false}, "line_render": {"visible": true, "color": 16711680, "linewidth": 4}}, "Point3D_N": {"type": "Point", "position": {"x": -2.4492935982947065e-15, "y": 40.0, "z": 0.0}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_N": {"type": "Label", "position": {"x": -2.4492935982947065e-15, "y": 40.0, "z": 0.0}, "text": "N", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "Point3D_S": {"type": "Point", "position": {"x": -2.4492935982947065e-15, "y": -40.0, "z": 0.0}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_S": {"type": "Label", "position": {"x": -2.4492935982947065e-15, "y": -40.0, "z": 0.0}, "text": "S", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "PlaneSurface_30": {"position": {"x": 0.0, "y": 0.0, "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": 255, "linewidth": 4}, "surface_render": {"visible": false}, "type": "PlaneSurface", "path": "Circle_29"}, "Circle_29": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 40.5, "y": 40.5}}}]}, "PlaneSurface_32": {"position": {"x": 0.0, "y": -17.534845871563096, "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_31"}, "Circle_31": {"type": "Path2D", "path": [{"absEllipse": {"center": {"x": 0.0, "y": 0.0}, "startAngle": 0, "endAngle": 6.28318530718, "radius": {"x": 36.45176185196668, "y": 36.45176185196668}}}]}, "Point3D_C": {"type": "Point", "position": {"x": 0.0, "y": 0.0, "z": 0.0}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_C": {"type": "Label", "position": {"x": 0.0, "y": 0.0, "z": 0.0}, "text": "C", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "Point3D_E": {"type": "Point", "position": {"x": -26.24236115962029, "y": 0.0, "z": -30.18838320891088}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_E": {"type": "Label", "position": {"x": -26.24236115962029, "y": 0.0, "z": -30.18838320891088}, "text": "E", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "Point3D_A": {"type": "Point", "position": {"x": -35.95176185196668, "y": -17.534845871563096, "z": 0.0}, "point_render": {"color": 0, "size": 64}, "label_render": {"color": 0}}, "Label_for_Point3D_A": {"type": "Label", "position": {"x": -35.95176185196668, "y": -17.534845871563096, "z": 0.0}, "text": "A", "position_offset": {"x": 0.0, "y": 3.3941125496954276, "z": 3.3941125496954276}, "label_render": {"color": 0}}, "Point3D_D": {"type": "Point", "position": {"x": -23.58647797109922, "y": -17.534845871563096, "z": -27.13313909556684}, "point_render": {"color": 16711680, "size": 128}, "label_render": {"color": 16711680}}, "Label_for_Point3D_D": {"type": "Label", "position": {"x": -23.58647797109922, "y": -17.534845871563096, "z": -27.13313909556684}, "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°
Méridien du point D
Équateur 0°
Parallèle du point D
N : Pôle nord
S : Pôle sud
C : Centre de la terre
D : Ville de Jaraguá do Sul

Sachant que \( \widehat{ABD} = 49 ° \), \( \widehat{SCE} = 90 ° \), \( \widehat{DCN} = 116 ° \) et \( \widehat{ECD} = 26 ° \), donner la latitude de la ville de Jaraguá do Sul (Brésil).
Exemples de format de réponses attendu : \(80°N\), \(60°S\), \(80°E\) ou \(20°O\)

Exercice 5 : Additionner 2 longueurs entières dans 2 unités différentes (du cm au dam), résultat en mm

Combien fait la somme de 53 cm et 10 m en mm ?

Revenir au choix du niveau