Các hệ thức lượng trong tam giác

Home Lớp 10 Toán lớp 10 - Sách Kết nối tri thức Bài 6: Các hệ thức lượng trong tam giácBài tập cơ bản

{"common":{"save":0,"post_id":"6430","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6419","mon_id":"1158767","chapter_id":"1158829","post_id":"6430","question":"Cho tam giác $ABC, AB=c,AC=b,BC=a$<\/span> . Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây \u0111úng?<\/p>","options":["A. $a^2=b^2+c^2+2bc\\cos A$<\/span> .","B. $a^2=b^2+c^2-2bc\\cos A$<\/span> .","C. $a^2=b^2+c^2-2bc\\cos C$<\/span> .","D. $a^2=b^2+c^2-2bc\\cos B$<\/span> ."],"correct":"2","level":"1","hint":"<svg height=\"222\" width=\"306\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"224\" id=\"canvas_background\" width=\"308\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><image height=\"222\" id=\"svg_1\" width=\"306\" x=\"0\" xlink:href=\"data:image\/png;base64,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\" y=\"0\"><\/image> <\/g> <\/svg><\/span><\/p>Theo \u0111\u1ecbnh lí Côsin trong tam giác ta có: Trong m\u1ed9t tam giác bình ph\u01b0\u01a1ng m\u1ed9t c\u1ea1nh b\u1eb1ng t\u1ed5ng bình ph\u01b0\u01a1ng hai c\u1ea1nh còn l\u1ea1i tr\u1eeb hai l\u1ea7n tích hai c\u1ea1nh \u0111ó nhân côsin c\u1ee7a góc xen gi\u1eefa hai c\u1ea1nh. Suy ra  $a^2=b^2+c^2-2bc\\cos A$<\/span> \u0111úng<\/p>","answer":"\u0110áp án: B<\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2023-03-05 13:56:35","option_type":"math","len":0},{"id":"6420","mon_id":"1158767","chapter_id":"1158829","post_id":"6430","question":"Cho tam giác ABC có $AC=6,BC=10$<\/span> , góc $C$<\/span>  b\u1eb1ng $120^o$<\/span> . \u0110\u1ed9 dài c\u1ea1nh $AB$<\/span>  là?<\/p>","options":["A. $AB=28$<\/span> .","B. $AB=14$<\/span> .","C. $AB=2\\sqrt{19}$<\/span> .","D. $AB=19\\sqrt{2}$<\/span> ."],"correct":"2","level":"1","hint":" <svg height=\"126\" width=\"303\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"128\" id=\"canvas_background\" width=\"305\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><image height=\"126\" id=\"svg_1\" width=\"303\" x=\"0\" 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y=\"0\"><\/image> <\/g> <\/svg><\/span> Áp d\u1ee5ng \u0111\u1ecbnh lí Côsin cho tam giác $ABC$<\/span>  ta có:  $AB^2=CA^2+CB^2-2CA.CB.\\cos C\\\\\\Rightarrow AB^2=6^2+10^2-2.6.10.\\cos C\\\\\\Rightarrow AB^2=196 \\Rightarrow AB=14$<\/span><\/p>","answer":"\u0110áp án : B<\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2023-03-05 14:07:05","option_type":"math","len":0},{"id":"6421","mon_id":"1158767","chapter_id":"1158829","post_id":"6430","question":"Cho $\\triangle MNP$<\/span> có $MN=6,MP=8,\\angle M=60^o$<\/span> . \u0110\u1ed9 dài c\u1ea1nh $NP$<\/span>  là:<\/p>","options":["A. $2\\sqrt{13}$<\/span> ","B. $3\\sqrt{12}$<\/span> ","C. $2\\sqrt{37}$<\/span>","D. $\\sqrt{20}$<\/span>"],"correct":"1","level":"1","hint":" <svg height=\"216\" width=\"309\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"218\" id=\"canvas_background\" width=\"311\" x=\"-1\" y=\"-1\"><\/rect> <g 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y=\"0\"><\/image> <\/g> <\/svg><\/span> Áp d\u1ee5ng \u0111\u1ecbnh lí Côsin cho $\\triangle MNP$<\/span>  ta có:  $NP^2=MN^2+MP^2-2.MN.MP.\\cos\\angle M$<\/span><\/p>Suy ra: $NP^2=6^2+8^2-2.6.8.\\cos60^o=52\\Rightarrow NP=2\\sqrt{13}$<\/span><\/p>","answer":"\u0110áp án : A<\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2023-03-05 14:16:11","option_type":"math","len":0}]}