{"id":92,"date":"2025-06-29T13:21:35","date_gmt":"2025-06-29T04:21:35","guid":{"rendered":"https:\/\/math-friend.com\/?p=92"},"modified":"2025-07-29T10:28:46","modified_gmt":"2025-07-29T01:28:46","slug":"%e4%b8%80%e6%a9%8b%e5%a4%a7%e5%ad%a6-%e5%85%a8%e3%81%a6%e3%81%ae%e8%a7%92%e3%81%aetan%e3%81%8c%e6%95%b4%e6%95%b0%e3%81%a8%e3%81%aa%e3%82%8b%e4%b8%89%e8%a7%92%e5%bd%a2","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=92","title":{"rendered":"\u3010\u4e00\u6a4b\u5927\u5b66\u5165\u8a66\u3011\u5168\u3066\u306e\u89d2\u306etan\u304c\u6574\u6570\u3068\u306a\u308b\u4e09\u89d2\u5f62(1984)"},"content":{"rendered":"\n<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n<p class=\"has-border -border02\">\\(\\triangle{ABC}\\)\u306b\u95a2\u3057\u3066, \\(\\tan{A}\\), \\(\\tan{B}\\), \\(\\tan{C}\\)\u304c\u3059\u3079\u3066\u6574\u6570\u3067\u3042\u308b\u3068\u304d, \u305d\u306e\u5024\u3092\u6c42\u3081\u3088. (1984 \u4e00\u6a4b\u5927\u5b66)<\/p>\n\n\n\n<p>\u4e00\u6a4b\u5927\u5b66\u306f\u6574\u6570\u554f\u984c\u306e\u826f\u554f\u304c\u591a\u304f, \u3053\u3061\u3089\u3082\u56f3\u5f62\u554f\u984c\u306b\u898b\u3048\u307e\u3059\u304c, \u5b9f\u306f\u6574\u6570\u554f\u984c\u3067\u3059. \\(\\tan\\)\u306f\u3069\u3093\u306a\u6574\u6570\u306e\u5024\u3092\u53d6\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067, \u7b54\u3048\u3082\u7121\u9650\u306b\u3042\u308a\u305d\u3046\u3067\u3059\u304c, \\(A, B, C\\)\u306f\u4e09\u89d2\u5f62\u306e3\u3064\u306e\u89d2\u3068\u3044\u3046\u3053\u3068\u3067, \u305d\u306e\u95a2\u4fc2\u5f0f\u304b\u3089\u7b54\u3048\u306f1\u3064\u306b\u306a\u308a\u307e\u3059. <br><br>\u3067\u306f\u89e3\u7b54\u306b\u53c2\u308a\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n<div class=\"wp-block-group is-style-crease\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\\(A\\leq B \\leq C\\)\u3068\u3057\u3066\u3082\u4e00\u822c\u6027\u3092\u5931\u308f\u306a\u3044.<br>\\(A, B, C\\)\u306f\u4e09\u89d2\u5f62\u306e3\u3064\u306e\u89d2\u3060\u304b\u3089, \\(A + B + C = 180\\,^\\circ\\)\u3067\u3042\u308b. \u3053\u306e\u95a2\u4fc2\u5f0f\u3068\u5148\u306e\u4e0d\u7b49\u5f0f\u3088\u308a, $$<br>180\\,^\\circ = A+B+C \\geq A+A+A=3A<br>$$\u3068\u306a\u308a, \u4e21\u8fba\u30923\u3067\u5272\u308b\u3053\u3068\u3067, \\(A\\geq 60\\,^\\circ\\)\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b.<br><br>\u3053\u3053\u3067, \u89d2\u5ea6\u304c\\(0\\,^\\circ\\)\u304b\u3089\\(90\\,^\\circ\\)\u306e\u9593\u3067\\(\\tan\\)\u306e\u30b0\u30e9\u30d5\u3092\u8003\u3048\u308b. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" width=\"1024\" height=\"779\" src=\"http:\/\/math-friend.com\/wp-content\/uploads\/2025\/06\/tan-1024x779.jpeg\" alt=\"\" class=\"wp-image-108\" style=\"width:589px;height:auto\" srcset=\"https:\/\/math-friend.com\/wp-content\/uploads\/2025\/06\/tan-1024x779.jpeg 1024w, https:\/\/math-friend.com\/wp-content\/uploads\/2025\/06\/tan-300x228.jpeg 300w, https:\/\/math-friend.com\/wp-content\/uploads\/2025\/06\/tan-768x584.jpeg 768w, https:\/\/math-friend.com\/wp-content\/uploads\/2025\/06\/tan.jpeg 1213w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p>\u3053\u306e\u7bc4\u56f2\u3067\u306f\u89d2\u5ea6\u304c\u5927\u304d\u304f\u306a\u308b\u306b\u3064\u308c\u3066\\(\\tan\\)\u306e\u5024\u306f\u5927\u304d\u304f\u306a\u308b(\u3053\u306e\u3088\u3046\u306a\u95a2\u6570\u306e\u6027\u8cea\u3092<strong>\u5358\u8abf\u5897\u52a0<\/strong>\u3068\u8a00\u3044\u307e\u3059). \\(A\\)\u306f\\(0\\,^\\circ\\)\u3088\u308a\u5927\u304d\u304f, \\(60\\,^\\circ\\)\u4ee5\u4e0b\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u304a\u308a, \\(\\tan{60\\,^\\circ}=\\sqrt{3}\\)\u3067\\(\\sqrt{3}= 1.73\\cdots \\)\u306f\\(2\\)\u3088\u308a\u5c0f\u3055\u3044\u305f\u3081, \u3053\u306e\u7bc4\u56f2\u3067\\(\\tan{A}\\)\u304c\u6574\u6570\u3068\u306a\u308b\u306e\u306f\\(A=45\\,^\\circ\\)\u306e\u6642\u306e\u307f\u3067, \\(\\tan{A}=1\\)\u3068\u306a\u308b. <br><br>\\(A=45\\,^\\circ\\)\u3068\u6c7a\u307e\u3063\u305f\u306e\u3067, \\(A+B+C=180\\,^\\circ\\)\u3088\u308a, \\(B+C=135\\,^\\circ\\)\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a, \u3053\u306e\u3053\u3068\u304b\u3089\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\\(\\triangle{ABC}\\)\u306f\u92ed\u89d2\u4e09\u89d2\u5f62\u3067\u3042\u308b\u3053\u3068\u304c\u8a00\u3048\u308b.<br><br>\\(A\\leq B\\)\u3088\u308a, \\(B\\geq 45\\,^\\circ\\)\u3067\u3042\u308b. \\(135\\,^\\circ =B+C\\leq 45\\,^\\circ + C\\)\u3088\u308a, \\(C\\leq 90\\,^\\circ\\)\u3068\u306a\u308b\u304c, \u554f\u984c\u306e\u5927\u524d\u63d0\u3088\u308a, \\(\\tan{C}\\)\u306f\u6574\u6570\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a, \\(C\\neq 90\\,^\\circ\\)\u304c\u5f97\u3089\u308c\u308b. \u3088\u3063\u3066, \\(\\triangle{ABC}\\)\u306e\u6700\u5927\u89d2\\(C\\)\u306f\\(C&lt;90\\,^\\circ\\)\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a, \\(\\triangle{ABC}\\)\u306f\u92ed\u89d2\u4e09\u89d2\u5f62\u3068\u306a\u308b.<br><br>\u4ee5\u4e0a\u304b\u3089, \\(45\\,^\\circ\\leq B\\leq C &lt; 90\\,^\\circ\\)\u3068\u306a\u308a, \u3053\u306e\u7bc4\u56f2\u3067\u306e\\(\\tan\\)\u306e\u30b0\u30e9\u30d5\u3088\u308a, \\(\\tan{B}\\), \\(\\tan{C}\\)\u306b\u95a2\u3059\u308b\u4e0d\u7b49\u5f0f, $$1\\leq \\tan{B}\\leq \\tan{C}$$\u304c\u5f97\u3089\u308c\u308b.<br><br>\u6b21\u306b, \\(\\tan{(B+C)}=\\tan{135\\,^\\circ}=-1\\)\u3067\u3042\u308b\u304c, \u3053\u308c\u306b\\(\\tan\\)\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u7528\u3044\u308b\u3068, $$\\frac{\\tan{B}+\\tan{C}}{1-\\tan{B}\\tan{C}}=-1$$\u3068\u306a\u308a, \u3053\u308c\u3092\u6574\u7406\u3059\u308b\u3068, $$\\tan{B}\\tan{C}-\\tan{B}-\\tan{C}-1=0$$\u3092\u5f97\u308b. \u3053\u308c\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u5f62\u3059\u308b\u3068, $$(\\tan{B}-1)(\\tan{C}-1)=2$$\u3068\u306a\u308a, \\(\\tan{B}-1\\)\u3082\\(\\tan{C}-1\\)\u3082\u6574\u6570\u3067\u3042\u308a, \u307e\u305f, $$1\\leq \\tan{B}\\leq \\tan{C}$$\u3067\u3042\u308b\u3053\u3068\u304b\u3089, \\(0&lt;\\tan{B}-1\\leq \\tan{C}-1\\)\u3067\u3042\u308b\u306e\u3067, \\(\\tan{B}-1=1\\), \\(\\tan{C}-1=2\\)\u306e\u307f\u304c\u8a31\u3055\u308c, \\(\\tan{B}=2\\), \\(\\tan{C}=3\\)\u3068\u306a\u308b. <br><br>\u5148\u306b\u5f97\u3066\u3044\u305f\\(\\tan{A}=1\\)\u3082\u52a0\u3048\u3066, $$\\tan{A}=1, \\tan{B}=2, \\tan{C}=3$$\u304c\u7b54\u3048\u3068\u306a\u308b.<\/p>\n<\/div><\/div>\n\n\n\n<p>\u4e0a\u306e\u89e3\u7b54\u3067, \\(A\\)\u306f\\(45\\,^\\circ\\)\u3067\u3042\u308b\u3053\u3068\u306f\u308f\u304b\u308a\u307e\u3059\u304c, \\(B\\)\u3068\\(C\\)\u306e\u89d2\u5ea6\u306f\u6574\u6570\u306b\u306a\u3089\u305a\u7c21\u5358\u306b\u306f\u66f8\u304d\u8868\u305b\u307e\u305b\u3093. \u5927\u5b66\u6570\u5b66\u3067\u306f\\(\\arctan\\)\u3068\u3044\u3046\u95a2\u6570\u3092\u4f7f\u3046\u3053\u3068\u3067, \\(B=\\arctan{2}\\), \\(C=\\arctan{3}\\)\u3068\u4e00\u5fdc\u8a18\u8ff0\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u3059\u304c, \u3053\u308c\u3089\u306f\u7279\u306b\u65b0\u3057\u3044\u60c5\u5831\u3092\u4e0e\u3048\u308b\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093. <br><br>\u95a2\u6570\u96fb\u5353\u306a\u3069\u3092\u7528\u3044\u308b\u3068\\(B\\), \\(C\\)\u306e\u8fd1\u4f3c\u5024\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u3066, \u8a08\u7b97\u3059\u308b\u3068\\(B=63.43\\cdots\\,^\\circ\\), \\(C=71.57\\cdots\\,^\\circ\\)\u3068\u306a\u308a, \u305f\u3057\u304b\u306b\\(A+B+C=180\\,^\\circ\\)\u3092\u6e80\u305f\u3057\u305d\u3046\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059.<\/p>\n\n\n\n<p>youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/LoRKeyxTFBk?si=nj8CcuXVTFoxUAfA\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n\n\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"<p>\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059. \\(\\triangle{ABC}\\)\u306b\u95a2\u3057\u3066, \\(\\tan{A}\\), \\(\\tan{B}\\), \\(\\tan{C}\\)\u304c\u3059\u3079\u3066\u6574\u6570\u3067\u3042\u308b\u3068\u304d, \u305d\u306e\u5024\u3092\u6c42\u3081\u3088. (1984 \u4e00\u6a4b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":121,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-92","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tokimakuru"],"_links":{"self":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/92","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=92"}],"version-history":[{"count":31,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/92\/revisions"}],"predecessor-version":[{"id":2026,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/posts\/92\/revisions\/2026"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=\/wp\/v2\/media\/121"}],"wp:attachment":[{"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=92"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=92"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math-friend.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=92"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}