{"id":4714,"date":"2022-09-01T13:45:01","date_gmt":"2022-09-01T11:45:01","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/goniometricke-funkce-priklad-2\/"},"modified":"2022-09-01T13:49:44","modified_gmt":"2022-09-01T11:49:44","slug":"goniometricke-funkce-priklad-2","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/goniometricke-funkce-priklad-2\/","title":{"rendered":"Goniometrick\u00e9 funkce &#8211; p\u0159\u00edklad 2"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed: <\/strong>St\u0159echa chalupy p\u0159ekr\u00fdv\u00e1 obytnou \u010d\u00e1st a k\u016flnu.&nbsp;Nejvy\u0161\u0161\u00ed st\u011bna m\u00e1 v\u00fd\u0161ku <strong><em>h<\/em><\/strong>. Rozm\u011bry jsou uveden\u00e9 v n\u00e1\u010drtku, st\u011bny s podlahou sv\u00edraj\u00ed prav\u00fd \u00fahel.<\/p>\n<p style=\"text-align: center\" data-mce-style=\"text-align: center;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone wp-image-4713\" src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/gonio-2-300x140.png\" alt=\"\" width=\"469\" height=\"219\" data-mce-src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/gonio-2-300x140.png\" srcset=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/gonio-2-300x140.png 300w, https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/09\/gonio-2.png 455w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p><strong>Jak\u00e1 je v\u00fd\u0161ka h nejvy\u0161\u0161\u00ed st\u011bny chalupy?<\/strong><br \/>a) men\u0161\u00ed ne\u017e 3,5 m<br \/>b) 3,5 m<br \/>c) 3,6 m<br \/>d) 3,7 m<br \/>e) v\u011bt\u0161\u00ed ne\u017e 3,7 m<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>1) Na obr\u00e1zku jsou 2 troj\u00faheln\u00edky, kter\u00e9 maj\u00ed shodn\u00fd \u00fahel a (vyu\u017e\u00edv\u00e1me tangens \u00fahlu a):<br \/>tg(a)= d\u00e9lka protilehl\u00e9 odv\u011bsny\/d\u00e9lka p\u0159ilehl\u00e9 odv\u011bsny<br \/>$$tg a=frac{0,6}{2,5}$$<\/p>\n<p>2) Vypo\u010d\u00edt\u00e1me si kolik m\u00e1 \u00b0:<br \/>a = 13,5\u00b0<\/p>\n<p>3) Nyn\u00ed dosad\u00edme do vzorce pro v\u00fdpo\u010det nejdel\u0161\u00ed strany:<br \/>$$tg 13,5=frac{x}{5}$$<\/p>\n<p>4) Vy\u0161lo n\u00e1m, o kolik je nejdel\u0161\u00ed strana del\u0161\u00ed ne\u017e druh\u00e1 nejdel\u0161\u00ed strana (2,3 m)<br \/>x = 1,2 m<\/p>\n<p>5)Te\u010f u\u017e jen se\u010dteme a z\u00edsk\u00e1me d\u00e9lku nejdel\u0161\u00ed strany h:<br \/>2,3 m + 1,2 m = 3,5 m<\/p>\n<p>Spr\u00e1vn\u00e1 odpov\u011b\u010f je tedy (b).<\/p>\n<p><br data-mce-bogus=\"1\"><\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 4-6 min<\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4714","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Goniometrick\u00e9 funkce - p\u0159\u00edklad 2 | 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\/goniometricke-funkce-priklad-2\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Goniometrick\u00e9 funkce - p\u0159\u00edklad 2 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: St\u0159echa chalupy p\u0159ekr\u00fdv\u00e1 obytnou \u010d\u00e1st a k\u016flnu.&nbsp;Nejvy\u0161\u0161\u00ed st\u011bna m\u00e1 v\u00fd\u0161ku h. Rozm\u011bry jsou uveden\u00e9 v n\u00e1\u010drtku, st\u011bny s podlahou sv\u00edraj\u00ed prav\u00fd \u00fahel. Jak\u00e1 je v\u00fd\u0161ka h nejvy\u0161\u0161\u00ed st\u011bny chalupy?a) men\u0161\u00ed ne\u017e 3,5 mb) 3,5 mc) 3,6 md) 3,7 me) v\u011bt\u0161\u00ed ne\u017e 3,7 m \u0158e\u0161en\u00ed: 1) Na obr\u00e1zku jsou 2 troj\u00faheln\u00edky, kter\u00e9 maj\u00ed shodn\u00fd \u00fahel ... 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