{"id":1019,"date":"2015-04-07T19:58:33","date_gmt":"2015-04-07T10:58:33","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1019"},"modified":"2021-11-04T08:55:35","modified_gmt":"2021-11-03T23:55:35","slug":"htb201302","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201302\/","title":{"rendered":"\u4e00\u6a4b\u59272013\uff1a\u7b2c2\u554f"},"content":{"rendered":"<hr \/>\n<p>\u5e73\u9762\u4e0a\u306e \\(4\\) \u70b9 O , A , B , C \u304c\r\n\\[\r\n\\text{OA} = 4 , \\ \\text{OB} = 3 , \\ \\text{OC} = 2 , \\ \\overrightarrow{\\text{OB}} \\cdot \\overrightarrow{\\text{OC}} = 3\r\n\\]\r\n\u3092\u6e80\u305f\u3059\u3068\u304d, \u25b3ABC \u306e\u9762\u7a4d\u306e\u6700\u5927\u5024\u3092\u6c42\u3081\u3088.<\/p>\r\n<hr \/>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p>\u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{OB}} \\cdot \\overrightarrow{\\text{OC}} & = 3 \\cdot 2 \\cdot \\cos \\angle \\text{BOC} = 3 \\\\\r\n\\text{\u2234} \\quad \\cos \\angle \\text{BOC} & = \\dfrac{1}{2} \\\\\r\n\\text{\u2234} \\quad \\angle \\text{BOC} & = 60^{\\circ}\r\n\\end{align}\\]\r\n\u25b3OBC \u306b\u5bfe\u3057\u3066, \u70b9 A \u306f\u70b9 O \u3092\u4e2d\u5fc3\u3068\u3059\u308b\u534a\u5f84 \\(4\\) \u306e\u5186\u5468\u4e0a\u3092\u52d5\u304f\u3068\u8003\u3048\u3089\u308c\u308b.<br \/>\r\n\u25b3ABC \u306e\u9762\u7a4d\u304c\u6700\u5927\u306b\u306a\u308b\u306e\u306f, \u70b9 A \u304c\u8fba BC \u304b\u3089\u3082\u3063\u3068\u3082\u96e2\u308c\u3066\u3044\u308b\u3068\u304d, \u3064\u307e\u308a \\(\\text{AO} \\perp \\text{BC}\\) \u3068\u306a\u308b\u3068\u304d\u3067\u3042\u308b.<br \/>\r\nAO \u306e\u5ef6\u9577\u7dda\u3068 BC \u306e\u4ea4\u70b9\u3092 H \u3068\u304a\u304f.\r\n\\[\r\n\\text{BC} = \\sqrt{2^2 +3^3 -2 \\cdot 2 \\cdot 3 \\cdot \\cos 60^{\\circ}} = \\sqrt{7}\r\n\\]\r\n\u25b3OBC \u306e\u9762\u7a4d\u306b\u7740\u76ee\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n\\dfrac{1}{2} \\cdot \\sqrt{7} \\text{OH} & = \\dfrac{1}{2} \\cdot 2 \\cdot 3 \\cdot \\sin 60^{\\circ} \\\\\r\n\\text{\u2234} \\quad \\text{OH} & = \\dfrac{3 \\sqrt{3}}{2 \\sqrt{7}}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u9762\u7a4d\u306e\u6700\u5927\u5024\u306f\r\n\\[\r\n\\dfrac{1}{2} \\cdot \\sqrt{7} \\left( \\dfrac{3 \\sqrt{3}}{2 \\sqrt{7}} +4 \\right) = \\underline{\\dfrac{3 \\sqrt{3}}{4} +2 \\sqrt{7}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5e73\u9762\u4e0a\u306e \\(4\\) \u70b9 O , A , B , C \u304c \\[ \\text{OA} = 4 , \\ \\text{OB} = 3 , \\ \\text{OC} = 2 , \\ \\overrightarrow{\\text{OB &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/htb201302\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[108],"tags":[146,111],"class_list":["post-1019","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2013","tag-hitotsubashi","tag-111"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1019","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=1019"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1019\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1019"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1019"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}