[{"data":1,"prerenderedAt":144},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Frazonamiento-matematico\u002Frumbos-y-orientacion?{}":3,"topics-with-content:razonamiento-matematico":102},{"course":4,"topic":12,"counts":17,"universities":22,"channels":31,"sampleQuestions":58,"sameName":101},{"id":5,"slug":6,"name":7,"shortName":8,"area":9,"icon":10,"sortOrder":11},17,"razonamiento-matematico","Razonamiento Matemático","R. Mat.","reasoning","i-lucide-puzzle",16,{"id":13,"courseId":5,"slug":14,"name":15,"sortOrder":16},1729,"rumbos-y-orientacion","Rumbos y orientación",28,{"topicId":13,"courseId":5,"questions":18,"classes":19,"videos":20,"minutes":21},12,59,50,715,[23],{"universityId":24,"questions":18,"years":25},1,[26,27,28,29,30],2026,2025,2024,2023,2022,[32,35,38,40,43,46,49,51,54,56],{"name":33,"classes":34},"Alberto Cruz",15,{"name":36,"classes":37},"Academia Grupo Ciencias",13,{"name":39,"classes":18},"Academia ipluton",{"name":41,"classes":42},"Ciclo Uni-San Marcos",5,{"name":44,"classes":45},"Academias Aduni y César Vallejo",4,{"name":47,"classes":48},"CEPRE UNMSM",3,{"name":50,"classes":48},"Salón Sapiens",{"name":52,"classes":53},"Academia_Pitagoras",2,{"name":55,"classes":24},"Saco Oliveros",{"name":57,"classes":24},"Trilce Multimedia",[59,84],{"id":60,"courseId":5,"topicId":13,"pastExamId":61,"stem":62,"options":63,"correctKey":65,"explanation":79,"difficulty":48,"status":80,"source":81,"stats":82},5304,252,"En un determinado instante, los puntos donde se encuentran ubicados los amigos Luis, Rosa, Teresa y Miguel coinciden con los vértices de un cuadrado cuyos lados miden 120 m. En ese instante, Luis observa a Rosa en la dirección N30°E, y Rosa, a su vez, observa a Teresa en la dirección N60°O. En dicho instante, Alfredo, hermano de Miguel, quien se encuentra en el punto central del cuadrado, observa a Rosa. ¿En qué dirección lo hace?",[64,67,70,73,76],{"key":65,"text":66},"A","N75°E",{"key":68,"text":69},"B","N45°E",{"key":71,"text":72},"C","N60°E",{"key":74,"text":75},"D","S30°E",{"key":77,"text":78},"E","S45°E","","published","UNMSM 2026-II · Área D · Ciencias Económicas y de la Gestión",{"attempts":83,"accuracy":83},0,{"id":85,"courseId":5,"topicId":13,"pastExamId":86,"stem":87,"options":88,"correctKey":74,"explanation":79,"difficulty":48,"status":80,"source":99,"stats":100},4344,237,"Un barco hace el siguiente recorrido: primero, 420 km en dirección este; luego, $120\\sqrt{3}$ km en dirección S30°E; después, 120 km en dirección S60°O y, finalmente, 180 km en dirección oeste, hasta llegar al punto $M$. Desde este punto, ¿en qué dirección tendrá que navegar este barco, para retornar a su punto de partida en el menor tiempo posible?",[89,91,93,95,97],{"key":65,"text":90},"N35°O",{"key":68,"text":92},"N30°O",{"key":71,"text":94},"N60°O",{"key":74,"text":96},"N45°O",{"key":77,"text":98},"N53°O","UNMSM 2025-II · Área A · Ciencias de la Salud",{"attempts":83,"accuracy":83},[],[103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,13,131,132,133,134,135,136,137,138,139,140,141,142,143],1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741,1742,1791501536236]