Một số hệ thức giữa cạnh, góc trong tam giác vuông và ứng dụng

Home Lớp 9 Toán lớp 9 - Sách Kết nối tri thức Bài 12. Một số hệ thức giữa cạnh, góc trong tam giác vuông và ứng dụngBài tập trung bình

{"common":{"save":0,"post_id":"7943","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"8376","post_id":"7943","mon_id":"1159278","chapter_id":"1159328","question":"Cho tam giác ΔABC vuông t\u1ea1i A . G\u1ecdi BC = a, AC = b, AB = c. Bi\u1ebft a = 20 cm, $\\widehat{B}=35^o$<\/span>. Ch\u1ecdn \u0111áp án \u0111úng<\/strong>.<\/p><svg height=\"150\" width=\"240\"> <g><title><\/title><rect fill=\"#fff\" height=\"152\" id=\"canvas_background\" width=\"242\" 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><g id=\"svg_12\"> <g id=\"svg_9\"> <path d=\"m24.28975,129.11874l0,-109l194,109l-194,0z\" fill=\"#5656ff\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <rect fill=\"#fff\" fill-opacity=\"null\" height=\"11\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"11\" x=\"24.40908\" y=\"117.43181\"><\/rect> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"2.40908\" xml:space=\"preserve\" y=\"130.43181\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"6.40908\" xml:space=\"preserve\" y=\"22.43181\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"220.40908\" xml:space=\"preserve\" y=\"126.43181\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_6\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"118.40908\" xml:space=\"preserve\" y=\"70.43181\">a<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"8.40908\" xml:space=\"preserve\" y=\"84.43181\">b<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"109.40908\" xml:space=\"preserve\" y=\"145.43181\">c<\/text> <\/g> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"20\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"138.40908\" xml:space=\"preserve\" y=\"125.43181\">35<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"15\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"161.40908\" xml:space=\"preserve\" y=\"111.43181\">o<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> b = 11,47 cm","B.<\/strong> b = 16,38 cm","C.<\/strong> c = 11,47 cm","D.<\/strong> a = 11,47 cm"],"correct":"1","level":"2","hint":"","answer":"Ch\u1ecdn A.<\/strong> b = 11,47 cm<\/span><\/p>Vì ΔABC vuông t\u1ea1i A nên $\\widehat{C}=90^o-\\widehat{B}=55^o$<\/span>.<\/p>b = a . sin B = 20 . sin 35° ≈ 11,47 (cm)<\/p>c = a . sin C = 20 . sin 55° ≈ 16,38 (cm) (Vì ΔABC vuông t\u1ea1i A nên sin C = cos B)<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-06 01:27:25","option_type":"txt","len":1},{"id":"8379","post_id":"7943","mon_id":"1159278","chapter_id":"1159328","question":"Cho tam giác ΔABC vuông t\u1ea1i A. Bi\u1ebft BC = 15 cm, AB = 10 cm. Ch\u1ecdn \u0111áp án \u0111úng<\/strong>.<\/p>","options":["A.<\/strong> $\\widehat{B}=42^o$<\/span>","B.<\/strong> $\\widehat{B}=40^o$<\/span>","C.<\/strong> $\\widehat{C}=42^o$<\/span>","D.<\/strong> $\\widehat{C}=48^o$<\/span>"],"correct":"3","level":"2","hint":"","answer":"Ch\u1ecdn C.<\/strong> $\\widehat{C}=42^o$<\/span><\/span><\/p><svg height=\"160\" width=\"210\"> <g><title><\/title><rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"212\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_10\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><path d=\"m29.10704,136.40511l0,-114l153.00001,114l-153.00001,0z\" fill=\"#56ff56\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\"><\/path> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"6.40908\" xml:space=\"preserve\" y=\"151.52272\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"10.40908\" xml:space=\"preserve\" y=\"22.52272\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"182.40908\" xml:space=\"preserve\" y=\"152.52272\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_5\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"101.40908\" xml:space=\"preserve\" y=\"70.52272\">15<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"’Times New Roman’, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"0.40908\" xml:space=\"preserve\" y=\"87.52272\">10<\/text> <rect fill=\"#fff\" fill-opacity=\"null\" height=\"12\" id=\"svg_8\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" width=\"12\" x=\"29.40908\" y=\"124.52272\"><\/rect> <\/g> <\/svg><\/span><\/p>Áp d\u1ee5ng \u0111\u1ecbnh lí Pythagore ta \u0111\u01b0\u1ee3c: $AC=\\sqrt{BC^2-AC^2}=5\\sqrt{5}$<\/span> (cm).<\/p>sin B = $\\dfrac{AC}{BC}=\\dfrac{5\\sqrt{5}}{15}$<\/span> suy ra $\\widehat{B}\\approx 48^o$<\/span> và $\\widehat{C}=90^o-\\widehat{B}\\approx 42^o$<\/span>.<\/p>","type":"choose","extra_type":"classic","time":"0","user_id":"127","test":"0","date":"2024-11-06 01:32:51","option_type":"math","len":0},{"id":"8381","post_id":"7943","mon_id":"1159278","chapter_id":"1159328","question":"Cho tam giác ΔABC vuông t\u1ea1i A . G\u1ecdi BC = a, AC = b, AB = c. Bi\u1ebft c = 3,8 cm, $\\widehat{B}=51^o$<\/span>. Ch\u1ecdn \u0111áp án \u0111úng<\/strong>.<\/p><svg height=\"140\" width=\"250\"> <g><title><\/title><rect fill=\"#fff\" height=\"142\" id=\"canvas_background\" width=\"252\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_5\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_3\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"231.40908\" xml:space=\"preserve\" y=\"117.43181\">B<\/text> <path d=\"m31.88702,169.27466l0,-107l185,107l-185,0z\" fill=\"#ffffaa\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"1.5\" transform=\"rotate(150.20481872558594 124.38702392578125,115.77465820312501) \"><\/path> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_2\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"169.40908\" xml:space=\"preserve\" y=\"22.43181\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_4\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"3.40908\" xml:space=\"preserve\" y=\"112.43181\">C<\/text> <rect fill=\"#5656ff\" height=\"10\" id=\"svg_7\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"1.5\" transform=\"rotate(150 176.40907287597653,30.431812286376946) \" width=\"10\" x=\"171.40908\" y=\"25.43181\"><\/rect> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"130.40908\" xml:space=\"preserve\" y=\"132.43181\">a<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"204.40908\" xml:space=\"preserve\" y=\"63.43181\">c<\/text> <text fill=\"#000000\" font-family=\"Times New Roman, Times, serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"91.40908\" xml:space=\"preserve\" y=\"61.43181\">b<\/text> <\/g> <\/svg><\/span><\/p>","options":["A.<\/strong> b = 4,2 cm","B.<\/strong> a = 6 cm","C.<\/strong> a = 4,6 cm","D.<\/strong> b = 6 cm"],"correct":"2","level":"2","hint":" <\/strong><\/p>","answer":"Ch\u1ecdn B.<\/strong> a = 6 cm<\/span><\/p>Xét tam giác ΔABC vuông t\u1ea1i A. Áp d\u1ee5ng h\u1ec7 th\u1ee9c gi\u1eefa c\u1ea1nh và góc trong tam giác vuông, ta có:<\/p>cos B = $\\dfrac{c}{a}$<\/span> hay cos 51° = $\\dfrac{3,8}{a}$<\/span> suy ra a = 6 cm.<\/p>Áp d\u1ee5ng \u0111\u1ecbnh lí Pythagore ta \u0111\u01b0\u1ee3c: $b=\\sqrt{a^2-c^2}\\approx \\sqrt{6^2-3,8^2}\\approx 4,6$<\/span> (cm).<\/p>","type":"choose","extra_type":"shape1","time":"0","user_id":"127","test":"0","date":"2024-11-06 01:41:52","option_type":"txt","len":0}]}