{"id":4513,"date":"2025-11-02T12:02:42","date_gmt":"2025-11-02T04:02:42","guid":{"rendered":"http:\/\/jhwk.online\/?p=4513"},"modified":"2025-11-08T22:07:02","modified_gmt":"2025-11-08T14:07:02","slug":"%e4%b8%89%e8%a7%92%e5%87%bd%e6%95%b0%e9%a2%98%e7%9b%ae1-2-2","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=4513","title":{"rendered":"\u4e09\u89d2\u51fd\u6570\u9898\u76ee2-1"},"content":{"rendered":"\n<div class=\"wp-block-stackable-subtitle stk-block-subtitle stk-block stk-8afe3d6\" data-block-id=\"8afe3d6\"><style>.stk-8afe3d6 .stk-block-subtitle__text{font-size:var(--stk--preset--font-size--medium, 20px) !important;color:#0693e3 !important;}@media screen and (max-width:999px){.stk-8afe3d6 .stk-block-subtitle__text{font-size:var(--stk--preset--font-size--medium, 20px) !important;}}<\/style><p class=\"stk-block-subtitle__text stk-subtitle has-text-color\">\u672c\u9898\u75312023\u7ea725\u73ed\u9ad8\u6893\u4fa8\u8bb2\u89e3\uff01<\/p><\/div>\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1728 \/ 1080;\" width=\"1728\" controls src=\"http:\/\/jhwk.online\/wp-content\/uploads\/2025\/11\/\u4e09\u89d2\u51fd\u6570\u9898\u76ee2-1.mp4\"><\/video><\/figure>\n\n\n\n<p>[ratemypost]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-vivid-cyan-blue-color has-alpha-channel-opacity has-vivid-cyan-blue-background-color has-background is-style-wide\"\/>\n\n\n\n<h5 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-8a052dbd5caa870510f1e594e9e095cf\">\u9898\u76ee\u5c55\u793a\u2014\u2014\u5148\u63a2\u7a76\u3001\u518d\u542c\u8bb2<\/h5>\n\n\n\n<h5>\u9898\u76ee2<\/h5>\n\n\u5728\u9510\u89d2$\\triangle ABC$\u4e2d\uff0c\u89d2$A$\uff0c$B$\uff0c$C$\u6240\u5bf9\u7684\u8fb9\u4e3a$a$\uff0c$b$\uff0c$c$\uff0c\u82e5$\\displaystyle\\frac{\\sin B\\sin C}{3\\sin A} = \\frac{\\cos A}{a} + \\frac{\\cos C}{c}$\u4e14$\\sin^2 A + \\sin^2 B &#8211; \\sin^2 C = \\sin A \\cdot \\sin B$\uff0c\u6c42$\\displaystyle\\frac{c^2}{a + b}$\u7684\u53d6\u503c\u8303\u56f4\u3002\n\n\n\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-background has-link-color has-medium-font-size wp-elements-9d0540021c94136dca84d09cf7cfb04a\" style=\"color:#1e4b69;background:linear-gradient(0deg,rgb(230,242,255) 0%,rgb(230,242,255) 16%,rgb(92,175,230) 100%)\">\u89e3\u9898\u63a2\u7a76\u2014\u2014\u70b9\u51fb\u76f4\u8fbe<\/h4>\n\n\n\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left;\n    background-color: #e6f2ff; \/* \u6de1\u84dd\u8272\u80cc\u666f *\/\n    border: none;\n    padding: 8px 12px;\n    border-radius: 4px;\n    transition: all 0.3s ease; \/* \u5e73\u6ed1\u8fc7\u6e21\u52a8\u753b *\/\n    font-size: 16px;\n  }\n  \n  .video-jump-btn:hover {\n    background-color: #cce0ff; \/* \u7565\u6df1\u7684\u84dd\u8272\u80cc\u666f *\/\n    transform: scale(1.02); \/* \u8f7b\u5fae\u653e\u5927\u6548\u679c *\/\n    box-shadow: 0 2px 4px rgba(0,0,0,0.1); \/* \u589e\u52a0\u8f7b\u5fae\u9634\u5f71 *\/\n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime = 0; document.querySelector('video').play();\">\n\u7b2c\u4e00\u6b65\uff1a\u6c42\u51fa\\( C= \\displaystyle\\frac{\\pi}{3} \\)\uff1b\n<\/button>\n\n\n\n<br>\n\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime =38; document.querySelector('video').play();\">\n    \u7b2c\u4e8c\u6b65\uff1a\u5f97\u51fa\\( c=2\\sqrt{3} \\);\n\n<\/button>\n\n\n\n<br>\n<style>\n  .video-jump-btn {\n    cursor: pointer;\n    text-align: left; \/* \u5de6\u5bf9\u9f50\u6587\u672c *\/\n   \n  }\n<\/style>\n\n<button class=\"video-jump-btn\" onclick=\"document.querySelector('video').currentTime =140; document.querySelector('video').play();\">\n\n\u7b2c\u4e09\u6b65\uff1a\\( \u89c2\u5bdf\u4e09\u89d2\u5f62ABC\u7684\u5916\u63a5\u5706\uff0c\u8ba1\u7b97a+b\u7684\u8303\u56f4 \\);\n\n<\/button>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848\u89e3\u6790<\/summary>\n\\(\\sin^{2}A + \\sin^{2}B &#8211; \\sin^{2}C = \\sin A\\sin B\\)<p> \\(\\Rightarrow a^{2} + b^{2} &#8211; c^{2} = ab\\)<p> \\(\\cos C = \\displaystyle \\frac{a^{2} + b^{2} &#8211; c^{2}}{2ab} = \\displaystyle \\frac{1}{2}\\)<p> \\(C \\in (0, \\pi) \\Rightarrow C = \\displaystyle \\frac{\\pi}{3}\\)<p> \\(\\because \\displaystyle \\frac{\\sin B\\sin C}{3\\sin A} = \\displaystyle \\frac{\\cos A}{a} + \\displaystyle \\frac{\\cos C}{c}\\)<p> \\(\\therefore \\displaystyle \\frac{\\displaystyle \\frac{b}{2R}\\sin C}{3\\displaystyle \\frac{a}{2R}} = \\displaystyle \\frac{c\\cos A + a\\cos C}{ac}\\)<p> \\(\\displaystyle \\frac{b\\sin \\displaystyle \\frac{\\pi}{3}}{3a} = \\displaystyle \\frac{c\\cos A + a\\cos C}{ac}\\)<p> \u5982\u56fe\uff1a\\(A\\)<p> \\(c\\cos A = AD\\)\uff0c\\(a\\cos C = CD\\)<p> \\(\\therefore c\\cos A + a\\cos C = AC = b\\)<p> \u5373\u539f\u5f0f\u4e3a\\(\\displaystyle \\frac{\\displaystyle \\frac{\\sqrt{3}}{2}b}{3a} = \\displaystyle \\frac{b}{ac}\\)<p> \\(\\Rightarrow \\displaystyle \\frac{\\sqrt{3}}{6} = \\displaystyle \\frac{1}{c}\\) \\(\\therefore c = 2\\sqrt{3}\\)<p> \\(C\\)\u4e3a\u5b9a\u89d2\\(\\displaystyle \\frac{\\pi}{3}\\)<p> \\(c\\)\u4e3a\u5b9a\u5f26\\(2\\sqrt{3} \\Rightarrow\\)\u5916\u63a5\u5706<p> \u5982\u56fe\uff0c\\(\\triangle ABC\\)\u4e3a\u7b49\u8fb9\\(\\triangle\\)\u65f6\\((a + b)_{\\max} = 4\\sqrt{3}\\)<p> \\(BC\\)\u4e3a\\(2R\\)\u5373\\(\\triangle ABC\\)\u4e3a\\(Rt\\triangle\\)\u65f6\\((a + b)_{\\min} = 6\\)<p> \\(\\therefore a + b \\in (6, 4\\sqrt{3}]\\)<p> \u5f53\\(a + b\\)\u6700\u5927\u65f6\\(\\displaystyle \\frac{c}{a + b}\\)\u6700\u5c0f<p> \\(\\therefore \\displaystyle \\frac{c^{2}}{a + b} \\in [\\sqrt{3}, 2)\\)<p>\n<\/details>\n\n\n\n \n","protected":false},"excerpt":{"rendered":"<p>\u672c\u9898\u75312023\u7ea725\u73ed\u9ad8\u6893\u4fa8\u8bb2\u89e3\uff01 [ratemypost] \u9898\u76ee\u5c55\u793a\u2014\u2014\u5148\u63a2\u7a76\u3001\u518d\u542c\u8bb2 \u9898\u76ee2 \u5728\u9510\u89d2$\\t [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4513","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4513","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4513"}],"version-history":[{"count":10,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4513\/revisions"}],"predecessor-version":[{"id":4615,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/4513\/revisions\/4615"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4513"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}