{"id":567225,"date":"2026-07-20T11:48:35","date_gmt":"2026-07-20T04:48:35","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567225"},"modified":"2026-07-21T14:59:29","modified_gmt":"2026-07-21T07:59:29","slug":"he-thuc-luong-trong-tam-giac","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/he-thuc-luong-trong-tam-giac\/","title":{"rendered":"H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c: \u0111\u1ecbnh l\u00fd cosin, sin, di\u1ec7n t\u00edch"},"content":{"rendered":"<p>H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c l\u00e0 t\u1eadp h\u1ee3p c\u00e1c c\u00f4ng th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh, g\u00f3c, \u0111\u01b0\u1eddng cao, \u0111\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n c\u1ee7a m\u1ed9t tam gi\u00e1c, g\u1ed3m \u0111\u1ecbnh l\u00fd cosin, \u0111\u1ecbnh l\u00fd sin v\u00e0 c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m c\u1ee7a H\u00ecnh h\u1ecdc l\u1edbp 10, gi\u00fap gi\u1ea3i b\u00e0i to\u00e1n t\u00ednh c\u1ea1nh, t\u00ednh g\u00f3c v\u00e0 di\u1ec7n t\u00edch tam gi\u00e1c ch\u1ec9 t\u1eeb v\u00e0i d\u1eef ki\u1ec7n ban \u0111\u1ea7u. N\u1ed9i dung d\u01b0\u1edbi \u0111\u00e2y t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 c\u00f4ng th\u1ee9c quan tr\u1ecdng nh\u1ea5t k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc \u0111\u1ec3 b\u1ea1n d\u1ec5 ghi nh\u1edb v\u00e0 \u00e1p d\u1ee5ng.<\/p>\n<h2>B\u1ea3ng t\u1ed5ng h\u1ee3p c\u00f4ng th\u1ee9c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c<\/h2>\n<p>B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y li\u1ec7t k\u00ea nhanh c\u00e1c c\u00f4ng th\u1ee9c ch\u00ednh, gi\u1ea3i th\u00edch chi ti\u1ebft c\u00f3 \u1edf t\u1eebng ph\u1ea7n b\u00ean d\u01b0\u1edbi.<\/p>\n<table>\n<thead>\n<tr>\n<th>H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng<\/th>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<th>\u1ee8ng d\u1ee5ng ch\u00ednh<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0110\u1ecbnh l\u00fd cosin<\/td>\n<td>a\u00b2 = b\u00b2 + c\u00b2 \u2212 2bc\u00b7cosA<\/td>\n<td>Bi\u1ebft 2 c\u1ea1nh + g\u00f3c xen gi\u1eefa, ho\u1eb7c bi\u1ebft 3 c\u1ea1nh<\/td>\n<\/tr>\n<tr>\n<td>\u0110\u1ecbnh l\u00fd sin<\/td>\n<td>a\/sinA = b\/sinB = c\/sinC = 2R<\/td>\n<td>T\u00ednh c\u1ea1nh, g\u00f3c ho\u1eb7c b\u00e1n k\u00ednh ngo\u1ea1i ti\u1ebfp R<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch (\u0111\u00e1y \u2013 chi\u1ec1u cao)<\/td>\n<td>S = \u00bd\u00b7a\u00b7h<sub>a<\/sub><\/td>\n<td>Bi\u1ebft \u0111\u00e1y v\u00e0 chi\u1ec1u cao t\u01b0\u01a1ng \u1ee9ng<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch (2 c\u1ea1nh \u2013 g\u00f3c xen gi\u1eefa)<\/td>\n<td>S = \u00bd\u00b7bc\u00b7sinA<\/td>\n<td>Bi\u1ebft hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch (c\u00f4ng th\u1ee9c Heron)<\/td>\n<td>S = \u221a[p(p\u2212a)(p\u2212b)(p\u2212c)]<\/td>\n<td>Bi\u1ebft ba c\u1ea1nh<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch \u2013 b\u00e1n k\u00ednh ngo\u1ea1i ti\u1ebfp<\/td>\n<td>S = abc \/ (4R)<\/td>\n<td>Bi\u1ebft ba c\u1ea1nh v\u00e0 R<\/td>\n<\/tr>\n<tr>\n<td>Di\u1ec7n t\u00edch \u2013 b\u00e1n k\u00ednh n\u1ed9i ti\u1ebfp<\/td>\n<td>S = p\u00b7r<\/td>\n<td>Bi\u1ebft n\u1eeda chu vi v\u00e0 r<\/td>\n<\/tr>\n<tr>\n<td>\u0110\u01b0\u1eddng trung tuy\u1ebfn<\/td>\n<td>m<sub>a<\/sub>\u00b2 = (2b\u00b2 + 2c\u00b2 \u2212 a\u00b2) \/ 4<\/td>\n<td>Bi\u1ebft ba c\u1ea1nh<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Trong \u0111\u00f3 p = (a + b + c)\/2 l\u00e0 n\u1eeda chu vi; R, r l\u00e0 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp v\u00e0 n\u1ed9i ti\u1ebfp tam gi\u00e1c ABC.<\/p>\n<h2>\u0110\u1ecbnh l\u00fd cosin trong tam gi\u00e1c<\/h2>\n<p>\u0110\u1ecbnh l\u00fd cosin d\u00f9ng \u0111\u1ec3 t\u00ednh m\u1ed9t c\u1ea1nh khi bi\u1ebft hai c\u1ea1nh c\u00f2n l\u1ea1i v\u00e0 g\u00f3c xen gi\u1eefa, ho\u1eb7c t\u00ednh m\u1ed9t g\u00f3c khi bi\u1ebft \u0111\u1ee7 ba c\u1ea1nh. V\u1edbi tam gi\u00e1c ABC c\u00f3 c\u00e1c c\u1ea1nh a, b, c l\u1ea7n l\u01b0\u1ee3t \u0111\u1ed1i di\u1ec7n c\u00e1c g\u00f3c A, B, C:<\/p>\n<ul>\n<li>a\u00b2 = b\u00b2 + c\u00b2 \u2212 2bc\u00b7cosA (t\u01b0\u01a1ng t\u1ef1 cho b\u00b2, c\u00b2 khi \u0111\u1ed5i vai tr\u00f2 c\u00e1c c\u1ea1nh, g\u00f3c).<\/li>\n<\/ul>\n<p>Suy ra c\u00f4ng th\u1ee9c t\u00ednh g\u00f3c: cosA = (b\u00b2 + c\u00b2 \u2212 a\u00b2) \/ (2bc). \u0110\u00e2y c\u0169ng l\u00e0 d\u1ea1ng m\u1edf r\u1ed9ng c\u1ee7a \u0111\u1ecbnh l\u00fd Pytago: khi g\u00f3c A = 90\u00b0 th\u00ec cosA = 0, h\u1ec7 th\u1ee9c tr\u1edf th\u00e0nh a\u00b2 = b\u00b2 + c\u00b2.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-567735 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-1.jpg\" alt=\"he-thuc-luong-trong-tam-giac-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u0110\u1ecbnh l\u00fd sin trong tam gi\u00e1c<\/h2>\n<p>\u0110\u1ecbnh l\u00fd sin li\u00ean h\u1ec7 gi\u1eefa m\u1ed7i c\u1ea1nh, sin c\u1ee7a g\u00f3c \u0111\u1ed1i di\u1ec7n v\u00e0 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c R:<\/p>\n<ul>\n<li>a\/sinA = b\/sinB = c\/sinC = 2R.<\/li>\n<\/ul>\n<p>C\u00f4ng th\u1ee9c n\u00e0y d\u00f9ng khi bi\u1ebft m\u1ed9t c\u1ea1nh v\u00e0 hai g\u00f3c, ho\u1eb7c \u0111\u1ec3 t\u00ednh b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp R. T\u1eeb \u0111\u00f3 suy ra a = 2R\u00b7sinA.<\/p>\n<p><strong>Xem th\u00eam: <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/chu-vi-tam-giac-vuong\/\" target=\"_blank\" rel=\"noopener\">Kh\u00e1m Ph\u00e1 C\u00f4ng Th\u1ee9c V\u00e0 C\u00e1ch T\u00ednh Chu Vi Tam Gi\u00e1c Vu\u00f4ng To\u00e0n Di\u1ec7n<\/a><\/strong><\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-567736 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-2.jpg\" alt=\"he-thuc-luong-trong-tam-giac-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c<\/h2>\n<p>Trong h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng, di\u1ec7n t\u00edch tam gi\u00e1c S c\u00f3 th\u1ec3 t\u00ednh theo nhi\u1ec1u c\u00e1ch kh\u00e1c nhau t\u00f9y d\u1eef ki\u1ec7n \u0111\u1ec1 b\u00e0i cho tr\u01b0\u1edbc:<\/p>\n<table>\n<thead>\n<tr>\n<th>Tr\u01b0\u1eddng h\u1ee3p<\/th>\n<th>C\u00f4ng th\u1ee9c di\u1ec7n t\u00edch<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Bi\u1ebft c\u1ea1nh v\u00e0 chi\u1ec1u cao<\/td>\n<td>S = \u00bd \u00b7 a \u00b7 h<sub>a<\/sub><\/td>\n<\/tr>\n<tr>\n<td>Bi\u1ebft hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa<\/td>\n<td>S = \u00bd \u00b7 b \u00b7 c \u00b7 sinA<\/td>\n<\/tr>\n<tr>\n<td>Bi\u1ebft ba c\u1ea1nh v\u00e0 b\u00e1n k\u00ednh ngo\u1ea1i ti\u1ebfp<\/td>\n<td>S = abc \/ (4R)<\/td>\n<\/tr>\n<tr>\n<td>Bi\u1ebft n\u1eeda chu vi v\u00e0 b\u00e1n k\u00ednh n\u1ed9i ti\u1ebfp<\/td>\n<td>S = p \u00b7 r<\/td>\n<\/tr>\n<tr>\n<td>Bi\u1ebft ba c\u1ea1nh (c\u00f4ng th\u1ee9c Heron)<\/td>\n<td>S = \u221a[p(p\u2212a)(p\u2212b)(p\u2212c)]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Trong \u0111\u00f3 p = (a + b + c)\/2 l\u00e0 n\u1eeda chu vi, r v\u00e0 R l\u00e0 b\u00e1n k\u00ednh n\u1ed9i ti\u1ebfp v\u00e0 ngo\u1ea1i ti\u1ebfp. Bi\u1ebft \u0111\u00e1y \u2013 chi\u1ec1u cao th\u00ec d\u00f9ng S = \u00bd\u00b7a\u00b7h<sub>a<\/sub>; ch\u1ec9 bi\u1ebft ba c\u1ea1nh th\u00ec d\u00f9ng Heron, kh\u00f4ng c\u1ea7n t\u00ednh g\u00f3c tr\u01b0\u1edbc.<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-567737\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-3.jpg\" alt=\"he-thuc-luong-trong-tam-giac-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c \u0111\u01b0\u1eddng trung tuy\u1ebfn<\/h2>\n<p>\u0110\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u0169ng l\u00e0 m\u1ed9t h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng h\u1eefu \u00edch. \u0110\u01b0\u1eddng trung tuy\u1ebfn m<sub>a<\/sub> xu\u1ea5t ph\u00e1t t\u1eeb \u0111\u1ec9nh A \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ea1nh a \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng:<\/p>\n<ul>\n<li>m<sub>a<\/sub>\u00b2 = (2b\u00b2 + 2c\u00b2 \u2212 a\u00b2) \/ 4 (t\u01b0\u01a1ng t\u1ef1 cho m<sub>b<\/sub>, m<sub>c<\/sub> khi \u0111\u1ed5i vai tr\u00f2 c\u00e1c c\u1ea1nh).<\/li>\n<\/ul>\n<p>C\u00f4ng th\u1ee9c n\u00e0y gi\u00fap t\u00ednh nhanh trung tuy\u1ebfn khi \u0111\u00e3 bi\u1ebft ba c\u1ea1nh, kh\u00f4ng c\u1ea7n d\u1ef1ng h\u00ecnh.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-567738 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-4.jpg\" alt=\"he-thuc-luong-trong-tam-giac-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>V\u00ed d\u1ee5 \u00e1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft<\/h2>\n<p>S\u00e1u v\u00ed d\u1ee5 d\u01b0\u1edbi \u0111\u00e2y \u00e1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c \u1edf tr\u00ean, c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc.<\/p>\n<p><strong>V\u00ed d\u1ee5 1: T\u00ednh c\u1ea1nh b\u1eb1ng \u0111\u1ecbnh l\u00fd cosin.<\/strong> \u0110\u1ec1 b\u00e0i: tam gi\u00e1c ABC c\u00f3 b = 5, c = 8, g\u00f3c A = 60\u00b0. T\u00ednh c\u1ea1nh a.<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: a\u00b2 = b\u00b2 + c\u00b2 \u2212 2bc\u00b7cosA.<\/li>\n<li>B\u01b0\u1edbc 2: a\u00b2 = 5\u00b2 + 8\u00b2 \u2212 2\u00b75\u00b78\u00b7cos60\u00b0 = 25 + 64 \u2212 40 = 49.<\/li>\n<li>B\u01b0\u1edbc 3: a = \u221a49 = 7.<\/li>\n<\/ul>\n<p><strong>V\u00ed d\u1ee5 2: T\u00ednh g\u00f3c b\u1eb1ng \u0111\u1ecbnh l\u00fd cosin.<\/strong> \u0110\u1ec1 b\u00e0i: tam gi\u00e1c ABC c\u00f3 a = 7, b = 5, c = 8. T\u00ednh g\u00f3c A.<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: cosA = (b\u00b2 + c\u00b2 \u2212 a\u00b2) \/ (2bc) = (25 + 64 \u2212 49) \/ 80 = 40\/80 = 0,5.<\/li>\n<li>B\u01b0\u1edbc 2: Suy ra g\u00f3c A = 60\u00b0 \u2014 kh\u1edbp v\u00ed d\u1ee5 1.<\/li>\n<\/ul>\n<p><strong>V\u00ed d\u1ee5 3: T\u00ednh b\u00e1n k\u00ednh ngo\u1ea1i ti\u1ebfp b\u1eb1ng \u0111\u1ecbnh l\u00fd sin.<\/strong> \u0110\u1ec1 b\u00e0i: tam gi\u00e1c ABC c\u00f3 a = 7, g\u00f3c A = 60\u00b0. T\u00ednh b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp R.<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: R = a \/ (2\u00b7sinA) = 7 \/ (2\u00b7sin60\u00b0) = 7\/\u221a3 = 7\u221a3\/3.<\/li>\n<li>B\u01b0\u1edbc 2: R \u2248 7 \u00d7 1,732 \/ 3 \u2248 4,04.<\/li>\n<\/ul>\n<p><strong>V\u00ed d\u1ee5 4: T\u00ednh di\u1ec7n t\u00edch khi bi\u1ebft hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa.<\/strong> \u0110\u1ec1 b\u00e0i: tam gi\u00e1c ABC c\u00f3 b = 6, c = 10, g\u00f3c A = 30\u00b0. T\u00ednh di\u1ec7n t\u00edch S.<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: S = \u00bd\u00b7b\u00b7c\u00b7sinA = \u00bd\u00b76\u00b710\u00b7sin30\u00b0 = \u00bd\u00b760\u00b70,5 = 15.<\/li>\n<\/ul>\n<p><strong>V\u00ed d\u1ee5 5: T\u00ednh di\u1ec7n t\u00edch b\u1eb1ng c\u00f4ng th\u1ee9c Heron.<\/strong> \u0110\u1ec1 b\u00e0i: tam gi\u00e1c ABC c\u00f3 ba c\u1ea1nh 3, 4, 5. T\u00ednh di\u1ec7n t\u00edch S.<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: N\u1eeda chu vi p = (3 + 4 + 5)\/2 = 6.<\/li>\n<li>B\u01b0\u1edbc 2: S = \u221a[6\u00b7(6\u22123)\u00b7(6\u22124)\u00b7(6\u22125)] = \u221a[6\u00b73\u00b72\u00b71] = \u221a36 = 6.<\/li>\n<li>B\u01b0\u1edbc 3: V\u00ec 3\u00b2 + 4\u00b2 = 5\u00b2 (tam gi\u00e1c vu\u00f4ng), ki\u1ec3m ch\u1ee9ng nhanh: S = \u00bd\u00b73\u00b74 = 6 \u2014 kh\u1edbp k\u1ebft qu\u1ea3 Heron.<\/li>\n<\/ul>\n<p><strong>V\u00ed d\u1ee5 6: T\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung tuy\u1ebfn.<\/strong> \u0110\u1ec1 b\u00e0i: tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A, AB = c = 3, AC = b = 4, c\u1ea1nh huy\u1ec1n BC = a = 5. T\u00ednh trung tuy\u1ebfn m<sub>a<\/sub> t\u1eeb \u0111\u1ec9nh A.<\/p>\n<ul>\n<li>B\u01b0\u1edbc 1: m<sub>a<\/sub>\u00b2 = (2b\u00b2 + 2c\u00b2 \u2212 a\u00b2)\/4 = (2\u00b716 + 2\u00b79 \u2212 25)\/4 = 25\/4 = 6,25.<\/li>\n<li>B\u01b0\u1edbc 2: m<sub>a<\/sub> = \u221a6,25 = 2,5 \u2014 \u0111\u00fang b\u1eb1ng n\u1eeda c\u1ea1nh huy\u1ec1n.<\/li>\n<\/ul>\n<p><strong>B\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n:<\/strong> Tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A c\u00f3 AB = 9, AC = 12. T\u00ednh c\u1ea1nh BC v\u00e0 di\u1ec7n t\u00edch. <em>\u0110\u00e1p s\u1ed1: BC = \u221a(9\u00b2 + 12\u00b2) = \u221a225 = 15; di\u1ec7n t\u00edch S = \u00bd\u00b79\u00b712 = 54.<\/em><\/p>\n<p><strong>Xem th\u00eam: <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-tron\/\" target=\"_blank\" rel=\"noopener\">C\u00f4ng Th\u1ee9c T\u00ednh Di\u1ec7n T\u00edch H\u00ecnh Tr\u00f2n: C\u00e1ch T\u00ednh, V\u00ed D\u1ee5 &amp; B\u00e0i T\u1eadp<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-567739 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-5.jpg\" alt=\"he-thuc-luong-trong-tam-giac-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/he-thuc-luong-trong-tam-giac-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>L\u01b0u \u00fd khi \u00e1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c<\/h2>\n<p>M\u1ed9t v\u00e0i l\u1ed7i th\u01b0\u1eddng g\u1eb7p khi\u1ebfn k\u1ebft qu\u1ea3 sai d\u00f9 nh\u1edb \u0111\u00fang c\u00f4ng th\u1ee9c:<\/p>\n<ul>\n<li>Nh\u1ea7m c\u1ea1nh v\u00e0 g\u00f3c \u0111\u1ed1i di\u1ec7n: c\u1ea1nh a \u0111\u1ed1i di\u1ec7n g\u00f3c A, c\u1ea1nh b \u0111\u1ed1i di\u1ec7n g\u00f3c B \u2014 nh\u1ea7m v\u1ecb tr\u00ed s\u1ebd sai to\u00e0n b\u1ed9 ph\u00e9p t\u00ednh.<\/li>\n<li>B\u1ea5m m\u00e1y t\u00ednh sai \u0111\u01a1n v\u1ecb g\u00f3c: c\u1ea7n \u0111\u00fang ch\u1ebf \u0111\u1ed9 \u0111\u1ed9 (degree) ho\u1eb7c radian theo \u0111\u1ec1 b\u00e0i.<\/li>\n<li>D\u00f9ng Heron m\u00e0 ch\u01b0a ki\u1ec3m tra b\u1ea5t \u0111\u1eb3ng th\u1ee9c tam gi\u00e1c (t\u1ed5ng hai c\u1ea1nh ph\u1ea3i l\u1edbn h\u01a1n c\u1ea1nh c\u00f2n l\u1ea1i).<\/li>\n<li>Nh\u1ea7m sin v\u1edbi cosin: sin d\u00f9ng khi bi\u1ebft c\u1ea1nh \u2013 g\u00f3c \u0111\u1ed1i di\u1ec7n, cosin d\u00f9ng khi bi\u1ebft hai c\u1ea1nh \u2013 g\u00f3c xen gi\u1eefa ho\u1eb7c \u0111\u1ee7 ba c\u1ea1nh.<\/li>\n<\/ul>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c<\/h2>\n<h3>\u0110\u1ecbnh l\u00fd cosin ph\u00e1t bi\u1ec3u th\u1ebf n\u00e0o?<\/h3>\n<p>a\u00b2 = b\u00b2 + c\u00b2 \u2212 2bc\u00b7cosA: b\u00ecnh ph\u01b0\u01a1ng m\u1ed9t c\u1ea1nh b\u1eb1ng t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng hai c\u1ea1nh kia tr\u1eeb hai l\u1ea7n t\u00edch c\u1ee7a ch\u00fang v\u1edbi cosin g\u00f3c xen gi\u1eefa.<\/p>\n<h3>\u0110\u1ecbnh l\u00fd sin d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?<\/h3>\n<p>D\u00f9ng \u0111\u1ec3 t\u00ednh c\u1ea1nh, g\u00f3c c\u00f2n thi\u1ebfu ho\u1eb7c b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp, theo h\u1ec7 th\u1ee9c a\/sinA = b\/sinB = c\/sinC = 2R.<\/p>\n<h3>C\u00f4ng th\u1ee9c Heron t\u00ednh di\u1ec7n t\u00edch th\u1ebf n\u00e0o?<\/h3>\n<p>S = \u221a[p(p\u2212a)(p\u2212b)(p\u2212c)], v\u1edbi p l\u00e0 n\u1eeda chu vi. Ch\u1ec9 c\u1ea7n bi\u1ebft ba c\u1ea1nh, kh\u00f4ng c\u1ea7n bi\u1ebft g\u00f3c.<\/p>\n<h3>\u0110\u1ecbnh l\u00fd cosin c\u00f3 li\u00ean quan g\u00ec \u0111\u1ebfn \u0111\u1ecbnh l\u00fd Pytago?<\/h3>\n<p>Khi g\u00f3c A = 90\u00b0 th\u00ec cosA = 0, \u0111\u1ecbnh l\u00fd cosin tr\u1edf th\u00e0nh a\u00b2 = b\u00b2 + c\u00b2, ch\u00ednh l\u00e0 \u0111\u1ecbnh l\u00fd Pytago trong tam gi\u00e1c vu\u00f4ng.<\/p>\n<h3>Khi n\u00e0o n\u00ean d\u00f9ng \u0111\u1ecbnh l\u00fd cosin, khi n\u00e0o n\u00ean d\u00f9ng \u0111\u1ecbnh l\u00fd sin?<\/h3>\n<p>D\u00f9ng cosin khi bi\u1ebft hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa, ho\u1eb7c bi\u1ebft \u0111\u1ee7 ba c\u1ea1nh. D\u00f9ng sin khi bi\u1ebft m\u1ed9t c\u1ea1nh v\u00e0 hai g\u00f3c, ho\u1eb7c c\u1ea7n t\u00ednh b\u00e1n k\u00ednh ngo\u1ea1i ti\u1ebfp.<\/p>\n<h3>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c n\u00e0o d\u1ec5 nh\u1edb v\u00e0 d\u00f9ng ph\u1ed5 bi\u1ebfn nh\u1ea5t?<\/h3>\n<p>S = \u00bd\u00b7\u0111\u00e1y\u00b7chi\u1ec1u cao d\u1ec5 nh\u1edb nh\u1ea5t khi bi\u1ebft \u0111\u00e1y v\u00e0 chi\u1ec1u cao; c\u00f4ng th\u1ee9c Heron ph\u1ed5 bi\u1ebfn khi ch\u1ec9 bi\u1ebft ba c\u1ea1nh m\u00e0 ch\u01b0a bi\u1ebft g\u00f3c.<\/p>\n<h3>H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng c\u00f3 g\u00ec kh\u00e1c v\u1edbi tam gi\u00e1c th\u01b0\u1eddng?<\/h3>\n<p>Tam gi\u00e1c vu\u00f4ng c\u00f3 th\u00eam h\u1ec7 th\u1ee9c ri\u00eang v\u1ec1 c\u1ea1nh g\u00f3c vu\u00f4ng, h\u00ecnh chi\u1ebfu, \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n; \u0111\u00e2y c\u0169ng l\u00e0 tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u1ee7a cosin khi g\u00f3c b\u1eb1ng 90\u00b0.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>T\u00f3m l\u1ea1i, h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c g\u1ed3m \u0111\u1ecbnh l\u00fd cosin, \u0111\u1ecbnh l\u00fd sin, c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch v\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn \u2014 \u0111\u1ee7 \u0111\u1ec3 gi\u1ea3i m\u1ecdi b\u00e0i to\u00e1n v\u1ec1 c\u1ea1nh, g\u00f3c, di\u1ec7n t\u00edch tam gi\u00e1c. N\u1eafm v\u1eefng b\u1ea3ng c\u00f4ng th\u1ee9c v\u00e0 luy\u1ec7n theo t\u1eebng b\u01b0\u1edbc nh\u01b0 c\u00e1c v\u00ed d\u1ee5 tr\u00ean, b\u1ea1n s\u1ebd t\u1ef1 tin x\u1eed l\u00fd m\u1ecdi d\u1ea1ng b\u00e0i h\u00ecnh h\u1ecdc l\u1edbp 10. M\u1eddi b\u1ea1n tham kh\u1ea3o th\u00eam c\u00e1c b\u00e0i <strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dinh-ly-cosin\/\" target=\"_blank\" rel=\"noopener\">\u0111\u1ecbnh l\u00fd cosin<\/a>, <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-tam-giac\/\" target=\"_blank\" rel=\"noopener\">di\u1ec7n t\u00edch tam gi\u00e1c<\/a><\/strong> v\u00e0 <strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cach-tinh-dien-tich-tam-giac-vuong\/\" target=\"_blank\" rel=\"noopener\">di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng<\/a><\/strong> tr\u00ean chuy\u00ean m\u1ee5c tin t\u1ee9c c\u1ee7a Ho\u00e0ng H\u00e0 Mobile.<\/p>\n<p><script type=\"application\/ld+json\">\n{\"@context\": \"https:\/\/schema.org\", \"@type\": \"FAQPage\", \"mainEntity\": [\n{\"@type\": \"Question\", \"name\": \"\u0110\u1ecbnh l\u00fd cosin ph\u00e1t bi\u1ec3u th\u1ebf n\u00e0o?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"a\u00b2 = b\u00b2 + c\u00b2 \u2212 2bc\u00b7cosA: b\u00ecnh ph\u01b0\u01a1ng m\u1ed9t c\u1ea1nh b\u1eb1ng t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng hai c\u1ea1nh kia tr\u1eeb hai l\u1ea7n t\u00edch c\u1ee7a ch\u00fang v\u1edbi cosin g\u00f3c xen gi\u1eefa.\"}},\n{\"@type\": \"Question\", \"name\": \"\u0110\u1ecbnh l\u00fd sin d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"D\u00f9ng \u0111\u1ec3 t\u00ednh c\u1ea1nh, g\u00f3c c\u00f2n thi\u1ebfu ho\u1eb7c b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp, theo h\u1ec7 th\u1ee9c a\/sinA = b\/sinB = c\/sinC = 2R.\"}},\n{\"@type\": \"Question\", \"name\": \"C\u00f4ng th\u1ee9c Heron t\u00ednh di\u1ec7n t\u00edch th\u1ebf n\u00e0o?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"S = \u221a[p(p\u2212a)(p\u2212b)(p\u2212c)], v\u1edbi p l\u00e0 n\u1eeda chu vi. Ch\u1ec9 c\u1ea7n bi\u1ebft ba c\u1ea1nh, kh\u00f4ng c\u1ea7n bi\u1ebft g\u00f3c.\"}},\n{\"@type\": \"Question\", \"name\": \"\u0110\u1ecbnh l\u00fd cosin c\u00f3 li\u00ean quan g\u00ec \u0111\u1ebfn \u0111\u1ecbnh l\u00fd Pytago?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"Khi g\u00f3c A = 90\u00b0 th\u00ec cosA = 0, \u0111\u1ecbnh l\u00fd cosin tr\u1edf th\u00e0nh a\u00b2 = b\u00b2 + c\u00b2, ch\u00ednh l\u00e0 \u0111\u1ecbnh l\u00fd Pytago trong tam gi\u00e1c vu\u00f4ng.\"}},\n{\"@type\": \"Question\", \"name\": \"Khi n\u00e0o n\u00ean d\u00f9ng \u0111\u1ecbnh l\u00fd cosin, khi n\u00e0o n\u00ean d\u00f9ng \u0111\u1ecbnh l\u00fd sin?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"D\u00f9ng cosin khi bi\u1ebft hai c\u1ea1nh v\u00e0 g\u00f3c xen gi\u1eefa, ho\u1eb7c bi\u1ebft \u0111\u1ee7 ba c\u1ea1nh. D\u00f9ng sin khi bi\u1ebft m\u1ed9t c\u1ea1nh v\u00e0 hai g\u00f3c, ho\u1eb7c c\u1ea7n t\u00ednh b\u00e1n k\u00ednh ngo\u1ea1i ti\u1ebfp.\"}},\n{\"@type\": \"Question\", \"name\": \"C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c n\u00e0o d\u1ec5 nh\u1edb v\u00e0 d\u00f9ng ph\u1ed5 bi\u1ebfn nh\u1ea5t?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"S = \u00bd\u00b7\u0111\u00e1y\u00b7chi\u1ec1u cao d\u1ec5 nh\u1edb nh\u1ea5t khi bi\u1ebft \u0111\u00e1y v\u00e0 chi\u1ec1u cao; c\u00f4ng th\u1ee9c Heron ph\u1ed5 bi\u1ebfn khi ch\u1ec9 bi\u1ebft ba c\u1ea1nh m\u00e0 ch\u01b0a bi\u1ebft g\u00f3c.\"}},\n{\"@type\": \"Question\", \"name\": \"H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng c\u00f3 g\u00ec kh\u00e1c v\u1edbi tam gi\u00e1c th\u01b0\u1eddng?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"Tam gi\u00e1c vu\u00f4ng c\u00f3 th\u00eam h\u1ec7 th\u1ee9c ri\u00eang v\u1ec1 c\u1ea1nh g\u00f3c vu\u00f4ng, h\u00ecnh chi\u1ebfu, \u0111\u01b0\u1eddng cao \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n; \u0111\u00e2y c\u0169ng l\u00e0 tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u1ee7a cosin khi g\u00f3c b\u1eb1ng 90\u00b0.\"}}\n]}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c l\u00e0 t\u1eadp h\u1ee3p c\u00e1c c\u00f4ng th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh, g\u00f3c, \u0111\u01b0\u1eddng cao, \u0111\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n c\u1ee7a m\u1ed9t tam gi\u00e1c, g\u1ed3m \u0111\u1ecbnh l\u00fd cosin, \u0111\u1ecbnh l\u00fd sin v\u00e0 c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m c\u1ee7a H\u00ecnh h\u1ecdc l\u1edbp [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":567734,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c","_yoast_wpseo_title":"H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c: c\u00f4ng th\u1ee9c","_yoast_wpseo_metadesc":"H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c g\u1ed3m \u0111\u1ecbnh l\u00fd cosin, \u0111\u1ecbnh l\u00fd sin v\u00e0 c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch. Xem \u0111\u1ea7y \u0111\u1ee7 c\u00f4ng th\u1ee9c, v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i t\u1ea1i Ho\u00e0ng H\u00e0 Mobile.","footnotes":""},"categories":[16],"tags":[],"class_list":["post-567225","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-thu-thuat"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c: c\u00f4ng th\u1ee9c<\/title>\n<meta name=\"description\" content=\"H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c g\u1ed3m \u0111\u1ecbnh l\u00fd cosin, \u0111\u1ecbnh l\u00fd sin v\u00e0 c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch. 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