{"id":240,"date":"2025-03-21T01:53:21","date_gmt":"2025-03-20T17:53:21","guid":{"rendered":"https:\/\/tilearn.space\/?p=240"},"modified":"2025-03-21T02:21:46","modified_gmt":"2025-03-20T18:21:46","slug":"2024%e5%b1%8a%e5%ae%9d%e5%b1%b1%e5%8c%ba%e5%88%9d%e4%b8%89%e4%ba%8c%e6%a8%a1%e6%95%b0%e5%ad%a6%e8%af%95%e5%8d%b7%e7%b2%be%e8%ae%b2%ef%bc%88%e7%ac%ac6%e9%a2%98%ef%bc%89","status":"publish","type":"post","link":"https:\/\/tilearn.space\/?p=240","title":{"rendered":"2024\u5c4a\u5b9d\u5c71\u533a\u521d\u4e09\u4e8c\u6a21\u6570\u5b66\u8bd5\u5377\u7cbe\u8bb2\uff08\u7b2c6\u9898\uff09"},"content":{"rendered":"

6. \u5982\u56fe1\uff0c\\(\\triangle ABC\\)\u4e2d\uff0c\\(\\angle C=90^\\circ\\), \\(AB=5\\), \\(\\tan B=\\frac{1}{2}\\)<\/span>\u3002\u5982\u679c\u4ee5\u70b9\\(C\\)\u4e3a\u5706\u5fc3\uff0c\u534a\u5f84\u4e3a\\(R\\)\u7684\u2299\\(C\\)\u4e0e\u7ebf\u6bb5\\(AB\\)\u6709\u4e24\u4e2a\u4ea4\u70b9\uff0c\u90a3\u4e48\u2299\\(C\\)\u7684\u534a\u5f84\\(R\\)\u7684\u53d6\u503c\u8303\u56f4\u662f\uff08 \uff09<\/strong>
\n[latexpage]
\n\\begin{tikzpicture}
\n% \u5b9a\u4e49\u4e09\u89d2\u5f62 ABC \u7684\u9876\u70b9
\n\\coordinate (C) at (0,0);
\n\\coordinate (A) at (0,2.236); % \\sqrt{5} \u2248 2.236
\n\\coordinate (B) at (4.472,0); % 2\\sqrt{5} \u2248 4.472
\n% \u7ed8\u5236\u4e09\u89d2\u5f62 ABC
\n\\draw (A) — (B) — (C) — cycle;
\n% \u6807\u6ce8\u9876\u70b9
\n\\node at (A) [above left] {$A$};
\n\\node at (B) [below right] {$B$};
\n\\node at (C) [below left] {$C$};
\n\\end{tikzpicture}<\/p>\n

(A) \\(2<R\\leqslant\\sqrt{5}\\);<\/p>\n

(B) \\(2\\leqslant R\\leqslant\\sqrt{5}\\);<\/p>\n

(C) \\(\\sqrt{5}\\leqslant R\\leqslant2\\sqrt{5}\\);<\/p>\n

(D) \\(0<R\\leqslant\\sqrt{5}\\).<\/p>\n

<\/div>\n

\u9898\u76ee\u89e3\u6790<\/h2>\n

\u9996\u5148\uff0c\u6211\u4eec\u6765\u590d\u4e60\u4e00\u4e0b\u76f8\u5173\u7684\u77e5\u8bc6\u70b9\uff1a<\/p>\n

    \n
  • \u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u6027\u8d28\uff1a<\/strong>\u5728\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u659c\u8fb9\u662f\u6700\u957f\u7684\u8fb9\uff0c\u4e14\u6ee1\u8db3\u52fe\u80a1\u5b9a\u7406\uff1a\\(a^2 + b^2 = c^2\\)\uff0c\u5176\u4e2d\\(c\\)\u4e3a\u659c\u8fb9\u3002<\/li>\n
  • \u6b63\u5207\u51fd\u6570\uff1a<\/strong>\\(\\tan B =\\)\u5bf9\u8fb9\/\u90bb\u8fb9<\/span>\u00a0\uff0c\u8fd9\u91cc\u6307\u7684\u662f\u5728\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u89d2\\(B\\)\u7684\u5bf9\u8fb9\u4e0e\u90bb\u8fb9\u7684\u6bd4\u503c\u3002<\/li>\n
  • \u5706\u4e0e\u76f4\u7ebf\u7684\u5173\u7cfb\uff1a<\/strong>\u5f53\u5706\u4e0e\u76f4\u7ebf\u76f8\u5207\u65f6\uff0c\u5706\u5fc3\u5230\u76f4\u7ebf\u7684\u8ddd\u79bb\u7b49\u4e8e\u5706\u7684\u534a\u5f84\uff1b\u5f53\u5706\u4e0e\u76f4\u7ebf\u76f8\u4ea4\u65f6\uff0c\u5706\u5fc3\u5230\u76f4\u7ebf\u7684\u8ddd\u79bb\u5c0f\u4e8e\u5706\u7684\u534a\u5f84\u3002<\/li>\n<\/ul>\n

    \u9898\u76ee\u8981\u6c42\u6211\u4eec\u6c42\u51fa\u4ee5\u70b9C\u4e3a\u5706\u5fc3\uff0c\u534a\u5f84\u4e3aR\u7684\u2299C\u4e0e\u7ebf\u6bb5AB\u6709\u4e24\u4e2a\u4ea4\u70b9\u65f6\uff0c\u534a\u5f84R\u7684\u53d6\u503c\u8303\u56f4\u3002<\/p>\n

    \u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u660e\u786e\u51e0\u4e2a\u5173\u952e\u70b9\uff1a<\/p>\n

      \n
    • \u25b3ABC\u662f\u4e00\u4e2a\u76f4\u89d2\u4e09\u89d2\u5f62\uff0c\u5176\u4e2d\u2220C=90\u00b0\u3002<\/li>\n
    • \u5df2\u77e5AB=5\uff0c\u4e14\\(\\tan B = \\frac{1}{2}\\)<\/span>\u3002<\/li>\n
    • \u4ee5\u70b9C\u4e3a\u5706\u5fc3\uff0c\u534a\u5f84\u4e3aR\u7684\u2299C\u4e0e\u7ebf\u6bb5AB\u6709\u4e24\u4e2a\u4ea4\u70b9\u3002<\/li>\n<\/ul>\n

      \u6839\u636e\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u5230\u4ee5\u4e0b\u4fe1\u606f\uff1a<\/p>\n

        \n
      • \u5728\u76f4\u89d2\u4e09\u89d2\u5f62\u4e2d\uff0c\u659c\u8fb9\u662f\u6700\u957f\u7684\u8fb9\uff0c\u56e0\u6b64AC\u548cBC\u5206\u522b\u662f\u4e24\u6761\u76f4\u89d2\u8fb9\u3002<\/li>\n
      • \u6839\u636e\u52fe\u80a1\u5b9a\u7406\uff0c\u6709\\(AB^2 = AC^2 + BC^2\\)<\/span>\u3002<\/li>\n
      • \u5df2\u77e5AB=5\uff0c\u6240\u4ee5\u6709\\(5^2 = AC^2 + BC^2\\)<\/span>\uff0c\u5373\\(25 = AC^2 + BC^2\\)<\/span>\u3002<\/li>\n
      • \u53c8\u56e0\u4e3a\\(\\tan B = \\frac{1}{2}\\)<\/span>\uff0c\u6240\u4ee5\u6709\\(\\frac{BC}{AC} = \\frac{1}{2}\\)<\/span>\uff0c\u5373\\(BC = \\frac{1}{2}AC\\)<\/span>\u3002<\/li>\n<\/ul>\n

        \u5c06\\(BC = \\frac{1}{2}AC\\)<\/span>\u4ee3\u5165\u5230\u52fe\u80a1\u5b9a\u7406\u4e2d\uff0c\u5f97\u5230\uff1a<\/p>\n

        \\(25 = AC^2 + \\left(\\frac{1}{2}AC\\right)^2\\)<\/span><\/p>\n

        \u89e3\u5f97\uff1a\\(AC = 2\\sqrt{5}\\), \\(BC = \\sqrt{5}\\)<\/span>\u3002<\/p>\n

        \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u9700\u8981\u786e\u5b9a\u2299C\u4e0e\u7ebf\u6bb5AB\u6709\u4e24\u4e2a\u4ea4\u70b9\u65f6\uff0c\u534a\u5f84R\u7684\u53d6\u503c\u8303\u56f4\u3002<\/p>\n

          \n
        • \u5f53\u2299C\u4e0e\u7ebf\u6bb5AB\u76f8\u5207\u65f6\uff0c\u534a\u5f84R\u6700\u5c0f\uff0c\u6b64\u65f6R\u7b49\u4e8e\u70b9C\u5230\u7ebf\u6bb5AB\u7684\u8ddd\u79bb\u3002<\/li>\n
        • \u5f53\u2299C\u4e0e\u7ebf\u6bb5AB\u76f8\u4ea4\u65f6\uff0c\u534a\u5f84R\u6700\u5927\uff0c\u6b64\u65f6R\u7b49\u4e8e\u70b9C\u5230\u7ebf\u6bb5AB\u7684\u8ddd\u79bb\u52a0\u4e0a\u7ebf\u6bb5AB\u7684\u4e00\u534a\u3002<\/li>\n<\/ul>\n

          \u70b9C\u5230\u7ebf\u6bb5AB\u7684\u8ddd\u79bb\u53ef\u4ee5\u901a\u8fc7\u5782\u7ebf\u6bb5\u516c\u5f0f\u8ba1\u7b97\u5f97\u51fa\uff1a<\/p>\n

          \\(d = \\frac{|AC \\cdot BC|}{AB} = \\frac{|2\\sqrt{5} \\cdot \\sqrt{5}|}{5} = 2\\)<\/span>\u3002<\/p>\n

          \u56e0\u6b64\uff0c\u5f53\u2299C\u4e0e\u7ebf\u6bb5AB\u76f8\u5207\u65f6\uff0c\u534a\u5f84R\u6700\u5c0f\u4e3a2\u3002<\/p>\n

          \u5f53\u2299C\u4e0e\u7ebf\u6bb5AB\u76f8\u4ea4\u65f6\uff0c\u534a\u5f84R\u6700\u5927\u4e3a\u70b9C\u5230\u7ebf\u6bb5AB\u7684\u8ddd\u79bb\u52a0\u4e0a\u7ebf\u6bb5AB\u7684\u4e00\u534a\uff0c\u5373\\(R = 2 + \\frac{5}{2} = \\frac{9}{2}\\)<\/span>\u3002<\/p>\n

          \u4f46\u662f\uff0c\u7531\u4e8e\u2299C\u662f\u4ee5\u70b9C\u4e3a\u5706\u5fc3\uff0c\u534a\u5f84\u4e3aR\u7684\u5706\uff0c\u6240\u4ee5R\u7684\u6700\u5927\u503c\u4e0d\u80fd\u8d85\u8fc7AC\u6216BC\u7684\u957f\u5ea6\uff0c\u5373R\u7684\u6700\u5927\u503c\u4e3a\u221a5\u3002<\/p>\n

          \u7efc\u4e0a\u6240\u8ff0\uff0c\u2299C\u7684\u534a\u5f84R\u7684\u53d6\u503c\u8303\u56f4\u662f2 < R \u2264 \u221a5\u3002<\/p>\n

          \u56e0\u6b64\uff0c\u6b63\u786e\u7b54\u6848\u662f(A) 2 < R \u2264 \u221a5\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

          6. \u5982\u56fe1\uff0c\\(\\triangle ABC\\)\u4e2d\uff0c\\(\\angle C=90^\\circ\\), \\(AB=5 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-240","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=240"}],"version-history":[{"count":12,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/240\/revisions"}],"predecessor-version":[{"id":252,"href":"https:\/\/tilearn.space\/index.php?rest_route=\/wp\/v2\/posts\/240\/revisions\/252"}],"wp:attachment":[{"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tilearn.space\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}