{"id":1919,"date":"2020-09-27T08:32:52","date_gmt":"2020-09-27T06:32:52","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=1919"},"modified":"2025-09-20T13:23:10","modified_gmt":"2025-09-20T11:23:10","slug":"winkel-am-rechtwinkligen-dreieck-sin-cos-tan","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=1919","title":{"rendered":"Winkel am rechtwinkligen Dreieck -sin, cos, tan"},"content":{"rendered":"\n<p class=\"has-text-align-center has-background\" style=\"background-color:#ffebeb\">F\u00fcr diese Lektion solltest Du unbedingt die<strong><a href=\"https:\/\/mathe-lernen.net\/?p=1150\"> Umstellung von Formeln<\/a><\/strong> und Gleichungen beherrschen!<\/p>\n\n\n\n<p class=\"has-text-align-center has-white-color has-primary-background-color has-text-color has-background\"><strong>Im Dreieck liegt dem kleinsten Winkel die k\u00fcrzeste Seite gegen\u00fcber. <br>Dem gr\u00f6\u00dften Winkel liegt die l\u00e4ngste Seite gegen\u00fcber!<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"Sinus: Einf\u00fchrung am rechtwinkligen Dreieck\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/RGpuYRvH\/width\/2550\/height\/1178\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/true\/rc\/false\/ld\/false\/sdz\/true\/ctl\/false\" width=\"800px\" height=\"378px\" style=\"border:0px;\"> <\/iframe><\/pre>\n\n\n\n<p class=\"has-black-color has-light-gray-background-color has-text-color has-background\">Im rechtwinkligen Dreieck gibt es 2 spitze Winkel. <br><br>F\u00fcr diese spitzen Winkel gilt:<\/p>\n\n\n\n<p class=\"has-white-color has-primary-background-color has-text-color has-background\"><strong>Ein Schenkel des Winkels ist die Hypotenuse des Dreiecks. <\/strong><br><br><strong>Der andere Schenkel wird<\/strong> <strong>Ankathete (AK) des Winkles genannt<\/strong>!<br><br><strong>Die dem Winkel gegen\u00fcberliegende Seite <\/strong>ist eine Kathete. Sie wird <strong>Gegenkathete<\/strong> <strong>(GK)<\/strong> <strong>des Winkels<\/strong> genannt!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"495\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_1-1024x495.jpg\" alt=\"\" class=\"wp-image-1920\" style=\"width:613px;height:295px\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_1-1024x495.jpg 1024w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_1-300x145.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_1-768x371.jpg 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_1.jpg 1217w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">F\u00fcr <strong>Alpha<\/strong> sind hier die Schenkel die Hypotenuse und die Seite b, damit ist <strong>Seite b auch die Ankathete<\/strong>.<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"516\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyrth2_2-1024x516.jpg\" alt=\"\" class=\"wp-image-1921\" style=\"width:580px;height:292px\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyrth2_2-1024x516.jpg 1024w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyrth2_2-300x151.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyrth2_2-768x387.jpg 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyrth2_2.jpg 1130w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">F\u00fcr <strong>Beta<\/strong> sind die Hypotenuse und die Seite a die Schenkel, damit ist <strong>Seite a die Ankathete von Winkel Beta<\/strong>.<\/figcaption><\/figure>\n\n\n\n<p class=\"has-text-align-center has-white-color has-primary-background-color has-text-color has-background\"><strong>F\u00fcr die Gr\u00f6\u00dfen am rechtwinkligen Dreieck gelten folgende Beziehungen und Rechenvorschriften!<\/strong><\/p>\n\n\n\n<p>Wenn <strong>x ein spitzer Winkel <\/strong>des rechtwinkligen Dreiecks ist:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"165\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_3-1024x165.jpg\" alt=\"\" class=\"wp-image-1922\" style=\"width:751px;height:120px\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_3-1024x165.jpg 1024w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_3-300x48.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_3-768x124.jpg 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_3-1536x247.jpg 1536w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/pyth2_3.jpg 1690w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-align-center has-white-color has-text-color has-background\" style=\"background-color:#ff0037\"><strong>Zwei der Gr\u00f6\u00dfen einer dieser obigen Gleichungen m\u00fcssen bekannt sein, <br>um die dritte Gr\u00f6\u00dfe in dieser Gleichung zu berechnen!<\/strong><\/p>\n\n\n\n<p class=\"has-light-gray-background-color has-background\">Beispiel Winkelberechnung:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"633\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/trigono_1_winkelberechnung-1024x633.jpg\" alt=\"\" class=\"wp-image-9565\" style=\"width:820px;height:auto\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/trigono_1_winkelberechnung-1024x633.jpg 1024w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/trigono_1_winkelberechnung-300x186.jpg 300w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/trigono_1_winkelberechnung-768x475.jpg 768w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/trigono_1_winkelberechnung-200x124.jpg 200w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2020\/09\/trigono_1_winkelberechnung.jpg 1237w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-text-align-center has-background\" style=\"background-color:#a1eda1\"><a href=\"https:\/\/mathe-lernen.net\/?p=9142\" target=\"_blank\" rel=\"noreferrer noopener\">Rechentest  &#8211; Winkelberechnung<\/a><\/p>\n\n\n\n<p><\/p>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_1919\" class=\"pvc_stats all  \" data-element-id=\"1919\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div> ","protected":false},"excerpt":{"rendered":"<p>F\u00fcr diese Lektion solltest Du unbedingt die Umstellung von Formeln und Gleichungen beherrschen! Im Dreieck liegt dem kleinsten Winkel die k\u00fcrzeste Seite gegen\u00fcber. Dem gr\u00f6\u00dften Winkel liegt die l\u00e4ngste Seite gegen\u00fcber! Im rechtwinkligen Dreieck gibt es 2 spitze Winkel. F\u00fcr diese spitzen Winkel gilt: Ein Schenkel des Winkels ist die Hypotenuse des Dreiecks. Der andere Schenkel wird Ankathete (AK) des<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_1919\" class=\"pvc_stats all  \" data-element-id=\"1919\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[986,987,52,57],"tags":[100,122,124,157,158,159,160,161,162,308,309,310],"class_list":["post-1919","post","type-post","status-publish","format-standard","hentry","category-dreiecke-sinussatz-kosinussatz","category-pythagoras","category-rechtwinklige-dreiecke","category-trigonometrie-dreiecke-und-vierecke","tag-winkel","tag-sinus","tag-dreieck","tag-hypotenuse","tag-kathete","tag-pythagoras","tag-satz","tag-rechter-winkel","tag-rechtwinklig","tag-trigonometrie","tag-kosinus","tag-tangens"],"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1919","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1919"}],"version-history":[{"count":2,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1919\/revisions"}],"predecessor-version":[{"id":9567,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1919\/revisions\/9567"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}