{"id":3007,"date":"2022-05-27T17:13:55","date_gmt":"2022-05-27T15:13:55","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/sinova-veta-vzorec\/"},"modified":"2022-05-29T15:51:42","modified_gmt":"2022-05-29T13:51:42","slug":"sinova-veta-vzorec","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/sinova-veta-vzorec\/","title":{"rendered":"Sinov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed"},"content":{"rendered":"<p><strong>Sinov\u00e1 v\u011bta plat\u00ed pro obecn\u00fd troj\u00faheln\u00edk a vypad\u00e1 n\u00e1sledovn\u011b:<\/strong><\/p>\n<p>$$\\frac{a}{\\sin\\alpha}=\\frac{b}{\\sin\\beta}=\\frac{c}{\\sin\\gamma}=2r$$<\/p>\n<p style=\"text-align: center\"><em><strong>r=polom\u011br kru\u017enice opsan\u00e9 \u0394 ABC<\/strong><\/em><\/p>\n<ul>\n<li><strong>Co n\u00e1m tato v\u011bta \u0159\u00edk\u00e1?<\/strong><\/li>\n<\/ul>\n<p>Pom\u011br jednotliv\u00fdch d\u00e9lek a protilehl\u00fdch \u00fahl\u016f v obecn\u00e9m troj\u00faheln\u00edku je konstantn\u00ed.<\/p>\n<ul>\n<li><strong>Upraven\u00e9 tvary sinov\u00e9 v\u011bty:<\/strong><\/li>\n<\/ul>\n<p>$$\\frac{a}{b}=\\frac{\\sin\\alpha}{\\sin\\beta}, \\frac{b}{c}=\\frac{\\sin\\beta}{\\sin\\gamma}, \\frac{c}{a}=\\frac{\\sin\\gamma}{\\sin\\alpha}$$<\/p>\n<ul>\n<li><strong>Sinov\u00e1 v\u011bta pro pravo\u00fahl\u00fd troj\u00faheln\u00edk:<\/strong><\/li>\n<\/ul>\n<p>Se znalost\u00ed goniometrick\u00fdch funkc\u00ed m\u016f\u017eeme sinovou v\u011btu upravit tak, aby platila tak\u00e9 pro pravo\u00fahl\u00fd troj\u00faheln\u00edk.<\/p>\n<p>Jak na to?<\/p>\n<p>Sta\u010d\u00ed si uv\u011bdomit, \u017ee <em><strong>sin(90)<\/strong><\/em> je roven jedn\u00e9.<\/p>\n<p>$$\\frac{a}{\\sin\\alpha}=\\frac{b}{\\sin\\beta}=\\frac{c}{\\sin\\gamma}$$<\/p>\n<p style=\"text-align: center\">pokud je \u00fahel<strong><em> \u03b3<\/em><\/strong> roven <strong><em>90\u00b0<\/em><\/strong>, m\u016f\u017eeme rovnost upravit n\u00e1sledovn\u011b:<\/p>\n<p>$$\\frac{a}{\\sin\\alpha}=\\frac{b}{\\sin\\beta}=\\frac{c}{1}$$<\/p>\n<p style=\"text-align: center\">po dal\u0161\u00ed \u00faprav\u011b dostaneme:<\/p>\n<p>$$\\frac{a}{\\sin\\alpha}=\\frac{b}{\\sin\\beta}=c$$<\/p>\n<ul>\n<li><strong>Kdy m\u016f\u017eeme sinovou v\u011btu vyu\u017e\u00edt?<\/strong><\/li>\n<\/ul>\n<p>Kdy\u017e jsou d\u00e1ny <strong>dva \u00fahly troj\u00faheln\u00edku<\/strong> a <strong>d\u00e9lka jedn\u00e9 jeho strany<\/strong> a maj\u00ed se dopo\u010d\u00edtat velikosti zb\u00fdvaj\u00edc\u00edch stran<\/p>\n<p>Kdy\u017e jsou zn\u00e1my <strong>d\u00e9lky dvou stran troj\u00faheln\u00edku<\/strong> <strong>a velikost vnit\u0159n\u00edho \u00fahlu kter\u00fd nesv\u00edraj\u00ed<\/strong>, a je t\u0159eba zjistit zb\u00fdvaj\u00edc\u00ed \u00fahly. Ale pozor, v t\u011bchto p\u0159\u00edpadech se m\u016f\u017ee st\u00e1t, \u017ee <strong>s pou\u017eit\u00edm sinovy v\u011bty dostaneme dvojici \u0159e\u0161en\u00ed<\/strong>, ale pouze jedno d\u00e1v\u00e1 sou\u010det \u00fahl\u016f 180\u00b0 a tedy umo\u017en\u00ed sestavit troj\u00faheln\u00edk a je tedy t\u00edm spr\u00e1vn\u00fdm \u0159e\u0161en\u00edm.<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-3007","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Sinov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/sinova-veta-vzorec\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sinov\u00e1 v\u011bta vzorec a vyu\u017eit\u00ed | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Sinov\u00e1 v\u011bta plat\u00ed pro obecn\u00fd troj\u00faheln\u00edk a vypad\u00e1 n\u00e1sledovn\u011b: $$frac{a}{sinalpha}=frac{b}{sinbeta}=frac{c}{singamma}=2r$$ r=polom\u011br kru\u017enice opsan\u00e9 \u0394 ABC Co n\u00e1m tato v\u011bta \u0159\u00edk\u00e1? Pom\u011br jednotliv\u00fdch d\u00e9lek a protilehl\u00fdch \u00fahl\u016f v obecn\u00e9m troj\u00faheln\u00edku je konstantn\u00ed. Upraven\u00e9 tvary sinov\u00e9 v\u011bty: $$frac{a}{b}=frac{sinalpha}{sinbeta}, frac{b}{c}=frac{sinbeta}{singamma}, frac{c}{a}=frac{singamma}{sinalpha}$$ Sinov\u00e1 v\u011bta pro pravo\u00fahl\u00fd troj\u00faheln\u00edk: Se znalost\u00ed goniometrick\u00fdch funkc\u00ed m\u016f\u017eeme sinovou v\u011btu upravit tak, aby platila tak\u00e9 ... 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Pom\u011br jednotliv\u00fdch d\u00e9lek a protilehl\u00fdch \u00fahl\u016f v obecn\u00e9m troj\u00faheln\u00edku je konstantn\u00ed. Upraven\u00e9 tvary sinov\u00e9 v\u011bty: $$frac{a}{b}=frac{sinalpha}{sinbeta}, frac{b}{c}=frac{sinbeta}{singamma}, frac{c}{a}=frac{singamma}{sinalpha}$$ Sinov\u00e1 v\u011bta pro pravo\u00fahl\u00fd troj\u00faheln\u00edk: Se znalost\u00ed goniometrick\u00fdch funkc\u00ed m\u016f\u017eeme sinovou v\u011btu upravit tak, aby platila tak\u00e9 ... 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