{"id":620588,"date":"2026-11-09T09:20:30","date_gmt":"2026-11-09T02:20:30","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=620588"},"modified":"2026-11-09T09:30:27","modified_gmt":"2026-11-09T02:30:27","slug":"goc-nhi-dien","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/goc-nhi-dien\/","title":{"rendered":"G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00ec? C\u00e1ch x\u00e1c \u0111\u1ecbnh v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i"},"content":{"rendered":"<p>G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 h\u00ecnh t\u1ea1o b\u1edfi hai n\u1eeda m\u1eb7t ph\u1eb3ng c\u00f3 chung b\u1edd l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng d; s\u1ed1 \u0111o c\u1ee7a n\u00f3 b\u1eb1ng s\u1ed1 \u0111o g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n, t\u1ee9c g\u00f3c t\u1ea1o b\u1edfi hai tia c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi d t\u1ea1i m\u1ed9t \u0111i\u1ec3m v\u00e0 l\u1ea7n l\u01b0\u1ee3t n\u1eb1m trong hai n\u1eeda m\u1eb7t ph\u1eb3ng. S\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n n\u1eb1m trong kho\u1ea3ng t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0. \u0110\u00e2y l\u00e0 n\u1ed9i dung To\u00e1n 11 ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi; b\u00e0i vi\u1ebft h\u01b0\u1edbng d\u1eabn c\u00e1ch x\u00e1c \u0111\u1ecbnh g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n, c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh v\u00e0 4 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i.<\/p>\n<h2>G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00ec?<\/h2>\n<p>G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 h\u00ecnh g\u1ed3m hai n\u1eeda m\u1eb7t ph\u1eb3ng (P) v\u00e0 (Q) c\u00f3 chung b\u1edd l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng d; d g\u1ecdi l\u00e0 c\u1ea1nh, c\u00f2n (P), (Q) l\u00e0 hai m\u1eb7t c\u1ee7a g\u00f3c nh\u1ecb di\u1ec7n. G\u00f3c nh\u1ecb di\u1ec7n \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 [P, d, Q], ho\u1eb7c [M, d, N] v\u1edbi M thu\u1ed9c (P), N thu\u1ed9c (Q) v\u00e0 M, N kh\u00f4ng n\u1eb1m tr\u00ean d.<\/p>\n<p>M\u1ed9t v\u00ed d\u1ee5 quen thu\u1ed9c l\u00e0 c\u00e1nh c\u1eeda m\u1edf ra so v\u1edbi b\u1ee9c t\u01b0\u1eddng: b\u1ea3n l\u1ec1 l\u00e0 c\u1ea1nh d, m\u1eb7t t\u01b0\u1eddng v\u00e0 m\u1eb7t c\u00e1nh c\u1eeda l\u00e0 hai m\u1eb7t c\u1ee7a g\u00f3c nh\u1ecb di\u1ec7n. M\u1edf c\u1eeda c\u00e0ng r\u1ed9ng, s\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n c\u00e0ng l\u1edbn, t\u1ed1i \u0111a c\u00f3 th\u1ec3 t\u1edbi 180\u00b0 khi c\u00e1nh c\u1eeda v\u00e0 b\u1ee9c t\u01b0\u1eddng th\u1eb3ng h\u00e0ng.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-622411 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-1.jpg\" alt=\"goc-nhi-dien-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>G\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n l\u00e0 g\u00ec v\u00e0 x\u00e1c \u0111\u1ecbnh nh\u01b0 th\u1ebf n\u00e0o?<\/h2>\n<p>G\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n l\u00e0 g\u00f3c xOy, trong \u0111\u00f3 O l\u00e0 m\u1ed9t \u0111i\u1ec3m tr\u00ean c\u1ea1nh d, tia Ox n\u1eb1m trong (P) v\u00e0 tia Oy n\u1eb1m trong (Q), c\u1ea3 hai c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi d. S\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n b\u1eb1ng s\u1ed1 \u0111o g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n v\u00e0 kh\u00f4ng ph\u1ee5 thu\u1ed9c v\u00e0o v\u1ecb tr\u00ed \u0111i\u1ec3m O tr\u00ean d.<\/p>\n<p>C\u00e1c b\u01b0\u1edbc x\u00e1c \u0111\u1ecbnh g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n [P, d, Q]:<\/p>\n<ol>\n<li>X\u00e1c \u0111\u1ecbnh c\u1ea1nh d (giao tuy\u1ebfn c\u1ee7a hai m\u1eb7t ph\u1eb3ng ch\u1ee9a hai m\u1eb7t).<\/li>\n<li>T\u00ecm m\u1ed9t \u0111i\u1ec3m A thu\u1ed9c (P) m\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a A xu\u1ed1ng (Q) l\u00e0 \u0111i\u1ec3m H d\u1ec5 x\u00e1c \u0111\u1ecbnh (th\u01b0\u1eddng do c\u00f3 \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng \u0111\u00e1y).<\/li>\n<li>T\u1eeb H k\u1ebb HO \u22a5 d (O \u2208 d). Theo \u0111\u1ecbnh l\u00fd ba \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c, AO \u22a5 d.<\/li>\n<li>G\u00f3c AOH (ho\u1eb7c g\u00f3c b\u00f9 c\u1ee7a n\u00f3, t\u00f9y hai m\u1eb7t n\u1eb1m c\u00f9ng hay kh\u00e1c ph\u00eda) l\u00e0 g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n; t\u00ednh b\u1eb1ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng AHO.<\/li>\n<\/ol>\n<p><img decoding=\"async\" class=\"size-full wp-image-622412 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-2.jpg\" alt=\"goc-nhi-dien-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>G\u00f3c nh\u1ecb di\u1ec7n kh\u00e1c g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng th\u1ebf n\u00e0o?<\/h2>\n<p>G\u00f3c nh\u1ecb di\u1ec7n c\u00f3 s\u1ed1 \u0111o t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0 v\u00e0 ph\u00e2n bi\u1ec7t hai m\u1eb7t c\u1ee5 th\u1ec3, c\u00f2n g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng ch\u1ec9 l\u1ea5y gi\u00e1 tr\u1ecb t\u1eeb 0\u00b0 \u0111\u1ebfn 90\u00b0. N\u1ebfu g\u00f3c nh\u1ecb di\u1ec7n c\u00f3 s\u1ed1 \u0111o \u03c6, th\u00ec g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng ch\u1ee9a n\u00f3 b\u1eb1ng \u03c6 khi \u03c6 \u2264 90\u00b0, v\u00e0 b\u1eb1ng 180\u00b0 \u2212 \u03c6 khi \u03c6 &gt; 90\u00b0.<\/p>\n<table>\n<thead>\n<tr>\n<th>Ti\u00eau ch\u00ed<\/th>\n<th>G\u00f3c nh\u1ecb di\u1ec7n<\/th>\n<th>G\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0110\u1ed1i t\u01b0\u1ee3ng<\/td>\n<td>Hai n\u1eeda m\u1eb7t ph\u1eb3ng chung b\u1edd<\/td>\n<td>Hai m\u1eb7t ph\u1eb3ng<\/td>\n<\/tr>\n<tr>\n<td>Kho\u1ea3ng gi\u00e1 tr\u1ecb<\/td>\n<td>0\u00b0 \u0111\u1ebfn 180\u00b0<\/td>\n<td>0\u00b0 \u0111\u1ebfn 90\u00b0<\/td>\n<\/tr>\n<tr>\n<td>K\u00fd hi\u1ec7u<\/td>\n<td>[P, d, Q]<\/td>\n<td>((P), (Q))<\/td>\n<\/tr>\n<tr>\n<td>\u1ee8ng d\u1ee5ng<\/td>\n<td>G\u00f3c gi\u1eefa hai m\u1eb7t b\u00ean c\u1ee7a kh\u1ed1i \u0111a di\u1ec7n<\/td>\n<td>\u0110\u1ed9 nghi\u00eang gi\u1eefa hai m\u1eb7t ph\u1eb3ng<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>C\u00f4ng th\u1ee9c t\u00ednh g\u00f3c nh\u1ecb di\u1ec7n th\u01b0\u1eddng d\u00f9ng<\/h2>\n<p>Ba c\u00e1ch t\u00ednh hay d\u00f9ng l\u00e0: t\u00ednh tr\u1ef1c ti\u1ebfp g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n b\u1eb1ng tam gi\u00e1c vu\u00f4ng, d\u00f9ng c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch h\u00ecnh chi\u1ebfu S&#8217; = S \u00b7 cos \u03c6, v\u00e0 d\u00f9ng vect\u01a1 ph\u00e1p tuy\u1ebfn trong h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz.<\/p>\n<ul>\n<li>Tam gi\u00e1c vu\u00f4ng: v\u1edbi g\u00f3c ph\u1eb3ng AOH vu\u00f4ng t\u1ea1i H, tan AOH = AH \/ OH.<\/li>\n<li>Di\u1ec7n t\u00edch h\u00ecnh chi\u1ebfu: n\u1ebfu \u0111a gi\u00e1c c\u00f3 di\u1ec7n t\u00edch S n\u1eb1m trong (P) v\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a n\u00f3 l\u00ean (Q) c\u00f3 di\u1ec7n t\u00edch S&#8217;, th\u00ec cos \u03c6 = S&#8217; \/ S v\u1edbi \u03c6 l\u00e0 g\u00f3c gi\u1eefa (P) v\u00e0 (Q). \u00dd t\u01b0\u1edfng h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c n\u00e0y c\u0169ng l\u00e0 n\u1ec1n t\u1ea3ng c\u1ee7a <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/khoang-cach-tu-diem-den-duong-thang\/\">kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng<\/a>.<\/li>\n<li>T\u1ecda \u0111\u1ed9 Oxyz: v\u1edbi vect\u01a1 ph\u00e1p tuy\u1ebfn n\u2081, n\u2082 c\u1ee7a hai m\u1eb7t ph\u1eb3ng, cos \u03c6 = |n\u2081 \u00b7 n\u2082| \/ (|n\u2081| \u00b7 |n\u2082|) cho g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng; sau \u0111\u00f3 c\u0103n c\u1ee9 h\u00ecnh v\u1ebd \u0111\u1ec3 quy\u1ebft \u0111\u1ecbnh g\u00f3c nh\u1ecb di\u1ec7n l\u00e0 \u03c6 hay 180\u00b0 \u2212 \u03c6.<\/li>\n<\/ul>\n<p>Mu\u1ed1n \u00f4n th\u00eam v\u1ec1 h\u00ecnh ch\u00f3p v\u00e0 l\u0103ng tr\u1ee5, xem c\u00e1c b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-khoi-chop\/\">th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p<\/a> v\u00e0 <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/hinh-lang-tru-dung\/\">h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng<\/a>.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-622413 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-3.jpg\" alt=\"goc-nhi-dien-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>V\u00ed d\u1ee5 t\u00ednh g\u00f3c nh\u1ecb di\u1ec7n c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<p>\u0110\u1ec1 chung (V\u00ed d\u1ee5 1\u20133): H\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh vu\u00f4ng c\u1ea1nh a, SA \u22a5 (ABCD) v\u00e0 SA = a.<\/p>\n<p>V\u00ed d\u1ee5 1: T\u00ednh s\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n [S, CD, A].<\/p>\n<ul>\n<li>CD \u22a5 AD (\u0111\u00e1y l\u00e0 h\u00ecnh vu\u00f4ng) v\u00e0 CD \u22a5 SA (v\u00ec SA \u22a5 \u0111\u00e1y) n\u00ean CD \u22a5 (SAD), suy ra CD \u22a5 SD.<\/li>\n<li>G\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n l\u00e0 g\u00f3c SDA.<\/li>\n<li>Trong tam gi\u00e1c SAD vu\u00f4ng t\u1ea1i A: tan SDA = SA \/ AD = a \/ a = 1, n\u00ean g\u00f3c SDA = 45\u00b0.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5 2: T\u00ednh s\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n [S, BD, A].<\/p>\n<ul>\n<li>G\u1ecdi O l\u00e0 t\u00e2m h\u00ecnh vu\u00f4ng: AO \u22a5 BD; BD \u22a5 SA n\u00ean BD \u22a5 (SAO), suy ra SO \u22a5 BD.<\/li>\n<li>G\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n l\u00e0 g\u00f3c SOA, v\u1edbi AO = a\u221a2 \/ 2.<\/li>\n<li>tan SOA = SA \/ AO = a \/ (a\u221a2\/2) = \u221a2, n\u00ean g\u00f3c SOA \u2248 54,74\u00b0.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5 3: T\u00ednh s\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n [B, SA, D].<\/p>\n<ul>\n<li>SA \u22a5 (ABCD) n\u00ean SA \u22a5 AB v\u00e0 SA \u22a5 AD.<\/li>\n<li>G\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n l\u00e0 g\u00f3c BAD = 90\u00b0.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5 4: T\u00ednh s\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n gi\u1eefa hai m\u1eb7t c\u1ee7a t\u1ee9 di\u1ec7n \u0111\u1ec1u ABCD c\u1ea1nh a (xem th\u00eam <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tu-dien-deu\/\">t\u00ednh ch\u1ea5t v\u00e0 c\u00f4ng th\u1ee9c t\u1ee9 di\u1ec7n \u0111\u1ec1u<\/a>), v\u00ed d\u1ee5 [A, BC, D].<\/p>\n<ul>\n<li>G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m BC: AM \u22a5 BC v\u00e0 DM \u22a5 BC (\u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c \u0111\u1ec1u), n\u00ean g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n l\u00e0 g\u00f3c AMD.<\/li>\n<li>AM = DM = a\u221a3 \/ 2, AD = a.<\/li>\n<li>Theo \u0111\u1ecbnh l\u00fd c\u00f4sin: cos AMD = (AM\u00b2 + DM\u00b2 \u2212 AD\u00b2) \/ (2 \u00b7 AM \u00b7 DM) = (3a\u00b2\/4 + 3a\u00b2\/4 \u2212 a\u00b2) \/ (2 \u00b7 3a\u00b2\/4) = 1\/3.<\/li>\n<li>V\u1eady g\u00f3c AMD \u2248 70,53\u00b0.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622414 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-4.jpg\" alt=\"goc-nhi-dien-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>L\u1ed7i th\u01b0\u1eddng g\u1eb7p khi x\u00e1c \u0111\u1ecbnh g\u00f3c nh\u1ecb di\u1ec7n<\/h2>\n<p>L\u1ed7i ph\u1ed5 bi\u1ebfn nh\u1ea5t l\u00e0 ch\u1ecdn hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh d t\u1ea1i m\u1ed9t \u0111i\u1ec3m, nh\u1ea7m g\u00f3c nh\u1ecb di\u1ec7n v\u1edbi g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng, v\u00e0 qu\u00ean tr\u01b0\u1eddng h\u1ee3p g\u00f3c t\u00f9.<\/p>\n<ul>\n<li>Hai tia ph\u1ea3i c\u00f9ng xu\u1ea5t ph\u00e1t t\u1eeb m\u1ed9t \u0111i\u1ec3m tr\u00ean c\u1ea1nh d v\u00e0 c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi d.<\/li>\n<li>Kh\u00f4ng t\u1ef1 \u0111\u1ed9ng l\u1ea5y g\u00f3c nh\u1ecdn: v\u1edbi g\u00f3c nh\u1ecb di\u1ec7n, k\u1ebft qu\u1ea3 c\u00f3 th\u1ec3 l\u1edbn h\u01a1n 90\u00b0.<\/li>\n<li>Ki\u1ec3m tra tam gi\u00e1c vu\u00f4ng: tr\u01b0\u1edbc khi d\u00f9ng tan, cos, ph\u1ea3i ch\u1ee9ng minh tam gi\u00e1c \u0111\u00f3 vu\u00f4ng.<\/li>\n<li>V\u1ebd h\u00ecnh r\u00f5 r\u00e0ng: n\u00e9t khu\u1ea5t v\u1ebd \u0111\u1ee9t \u0111\u1ec3 kh\u00f4ng ch\u1ecdn nh\u1ea7m m\u1eb7t ph\u1eb3ng.<\/li>\n<\/ul>\n<p>V\u1edbi h\u00ecnh l\u1eadp ph\u01b0\u01a1ng, b\u1ea1n c\u00f3 th\u1ec3 luy\u1ec7n th\u00eam b\u1eb1ng c\u00e1ch t\u00ednh c\u00e1c g\u00f3c nh\u1ecb di\u1ec7n gi\u1eefa m\u1eb7t ch\u00e9o v\u00e0 m\u1eb7t \u0111\u00e1y; \u00f4n k\u00edch th\u01b0\u1edbc h\u00ecnh l\u1eadp ph\u01b0\u01a1ng t\u1ea1i b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/the-tich-hinh-lap-phuong\/\">th\u1ec3 t\u00edch h\u00ecnh l\u1eadp ph\u01b0\u01a1ng<\/a>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622415 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-5.jpg\" alt=\"goc-nhi-dien-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/goc-nhi-dien-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 g\u00f3c nh\u1ecb di\u1ec7n<\/h2>\n<h3>G\u00f3c nh\u1ecb di\u1ec7n c\u00f3 s\u1ed1 \u0111o trong kho\u1ea3ng n\u00e0o?<\/h3>\n<p>S\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n n\u1eb1m trong kho\u1ea3ng t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0, kh\u00e1c v\u1edbi g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng ch\u1ec9 t\u1eeb 0\u00b0 \u0111\u1ebfn 90\u00b0.<\/p>\n<h3>G\u00f3c nh\u1ecb di\u1ec7n h\u1ecdc l\u1edbp m\u1ea5y?<\/h3>\n<p>Theo ch\u01b0\u01a1ng tr\u00ecnh gi\u00e1o d\u1ee5c ph\u1ed5 th\u00f4ng m\u1edbi, g\u00f3c nh\u1ecb di\u1ec7n \u0111\u01b0\u1ee3c h\u1ecdc trong ph\u1ea7n quan h\u1ec7 vu\u00f4ng g\u00f3c trong kh\u00f4ng gian c\u1ee7a To\u00e1n 11.<\/p>\n<h3>L\u00e0m sao x\u00e1c \u0111\u1ecbnh g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n?<\/h3>\n<p>Ch\u1ecdn m\u1ed9t \u0111i\u1ec3m O tr\u00ean c\u1ea1nh d, k\u1ebb hai tia trong hai m\u1eb7t c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi d t\u1ea1i O; g\u00f3c gi\u1eefa hai tia \u0111\u00f3 l\u00e0 g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n.<\/p>\n<h3>G\u00f3c nh\u1ecb di\u1ec7n c\u1ee7a t\u1ee9 di\u1ec7n \u0111\u1ec1u b\u1eb1ng bao nhi\u00eau?<\/h3>\n<p>G\u00f3c nh\u1ecb di\u1ec7n gi\u1eefa hai m\u1eb7t c\u1ee7a t\u1ee9 di\u1ec7n \u0111\u1ec1u c\u00f3 c\u00f4sin b\u1eb1ng 1\/3, t\u1ee9c x\u1ea5p x\u1ec9 70,53\u00b0.<\/p>\n<h3>K\u00fd hi\u1ec7u [S, CD, A] ngh\u0129a l\u00e0 g\u00ec?<\/h3>\n<p>\u0110\u00f3 l\u00e0 g\u00f3c nh\u1ecb di\u1ec7n c\u00f3 c\u1ea1nh CD, m\u1ed9t m\u1eb7t ch\u1ee9a \u0111i\u1ec3m S (m\u1eb7t SCD) v\u00e0 m\u1eb7t c\u00f2n l\u1ea1i ch\u1ee9a \u0111i\u1ec3m A (m\u1eb7t ACD, t\u1ee9c m\u1eb7t \u0111\u00e1y).<\/p>\n<h3>C\u00f3 th\u1ec3 t\u00ednh g\u00f3c nh\u1ecb di\u1ec7n b\u1eb1ng t\u1ecda \u0111\u1ed9 Oxyz kh\u00f4ng?<\/h3>\n<p>C\u00f3. T\u00ednh g\u00f3c gi\u1eefa hai vect\u01a1 ph\u00e1p tuy\u1ebfn \u0111\u1ec3 c\u00f3 g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng, r\u1ed3i c\u0103n c\u1ee9 v\u00e0o h\u00ecnh \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh g\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00f3c \u0111\u00f3 hay g\u00f3c b\u00f9.<br \/>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"G\u00f3c nh\u1ecb di\u1ec7n c\u00f3 s\u1ed1 \u0111o trong kho\u1ea3ng n\u00e0o?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"S\u1ed1 \u0111o g\u00f3c nh\u1ecb di\u1ec7n n\u1eb1m trong kho\u1ea3ng t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0, kh\u00e1c v\u1edbi g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng ch\u1ec9 t\u1eeb 0\u00b0 \u0111\u1ebfn 90\u00b0.\"}},{\"@type\":\"Question\",\"name\":\"G\u00f3c nh\u1ecb di\u1ec7n h\u1ecdc l\u1edbp m\u1ea5y?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Theo ch\u01b0\u01a1ng tr\u00ecnh gi\u00e1o d\u1ee5c ph\u1ed5 th\u00f4ng m\u1edbi, g\u00f3c nh\u1ecb di\u1ec7n \u0111\u01b0\u1ee3c h\u1ecdc trong ph\u1ea7n quan h\u1ec7 vu\u00f4ng g\u00f3c trong kh\u00f4ng gian c\u1ee7a To\u00e1n 11.\"}},{\"@type\":\"Question\",\"name\":\"L\u00e0m sao x\u00e1c \u0111\u1ecbnh g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Ch\u1ecdn m\u1ed9t \u0111i\u1ec3m O tr\u00ean c\u1ea1nh d, k\u1ebb hai tia trong hai m\u1eb7t c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi d t\u1ea1i O; g\u00f3c gi\u1eefa hai tia \u0111\u00f3 l\u00e0 g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n.\"}},{\"@type\":\"Question\",\"name\":\"G\u00f3c nh\u1ecb di\u1ec7n c\u1ee7a t\u1ee9 di\u1ec7n \u0111\u1ec1u b\u1eb1ng bao nhi\u00eau?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"G\u00f3c nh\u1ecb di\u1ec7n gi\u1eefa hai m\u1eb7t c\u1ee7a t\u1ee9 di\u1ec7n \u0111\u1ec1u c\u00f3 c\u00f4sin b\u1eb1ng 1\/3, t\u1ee9c x\u1ea5p x\u1ec9 70,53\u00b0.\"}},{\"@type\":\"Question\",\"name\":\"K\u00fd hi\u1ec7u [S, CD, A] ngh\u0129a l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\u0110\u00f3 l\u00e0 g\u00f3c nh\u1ecb di\u1ec7n c\u00f3 c\u1ea1nh CD, m\u1ed9t m\u1eb7t ch\u1ee9a \u0111i\u1ec3m S (m\u1eb7t SCD) v\u00e0 m\u1eb7t c\u00f2n l\u1ea1i ch\u1ee9a \u0111i\u1ec3m A (m\u1eb7t ACD, t\u1ee9c m\u1eb7t \u0111\u00e1y).\"}},{\"@type\":\"Question\",\"name\":\"C\u00f3 th\u1ec3 t\u00ednh g\u00f3c nh\u1ecb di\u1ec7n b\u1eb1ng t\u1ecda \u0111\u1ed9 Oxyz kh\u00f4ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"C\u00f3. T\u00ednh g\u00f3c gi\u1eefa hai vect\u01a1 ph\u00e1p tuy\u1ebfn \u0111\u1ec3 c\u00f3 g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng, r\u1ed3i c\u0103n c\u1ee9 v\u00e0o h\u00ecnh \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh g\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00f3c \u0111\u00f3 hay g\u00f3c b\u00f9.\"}}]}<\/script><\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00f3c gi\u1eefa hai n\u1eeda m\u1eb7t ph\u1eb3ng chung c\u1ea1nh d, \u0111o b\u1eb1ng g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n t\u1ea1o b\u1edfi hai tia c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi d t\u1ea1i m\u1ed9t \u0111i\u1ec3m, c\u00f3 gi\u00e1 tr\u1ecb t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0. Khi l\u00e0m b\u00e0i, h\u00e3y t\u00ecm \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh d nh\u1edd quan h\u1ec7 vu\u00f4ng g\u00f3c c\u00f3 s\u1eb5n trong h\u00ecnh, d\u00f9ng \u0111\u1ecbnh l\u00fd ba \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c v\u00e0 tam gi\u00e1c vu\u00f4ng \u0111\u1ec3 t\u00ednh. Luy\u1ec7n k\u1ef9 b\u1ed1n v\u00ed d\u1ee5 tr\u00ean l\u00e0 b\u1ea1n n\u1eafm \u0111\u01b0\u1ee3c c\u00e1c d\u1ea1ng g\u00f3c nh\u1ecb di\u1ec7n c\u01a1 b\u1ea3n c\u1ee7a To\u00e1n 11.<\/p>\n<p><strong>Xem th\u00eam:<\/strong><\/p>\n<ul>\n<li class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-huu-ti-la-gi\/\">S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec? S\u1ed1 v\u00f4 t\u1ec9 l\u00e0 g\u00ec? \u0110\u1eb7c tr\u01b0ng c\u1ee7a c\u00e1c s\u1ed1 trong To\u00e1n h\u1ecdc<\/a><\/li>\n<li class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-thuc-la-gi\/\">S\u1ed1 th\u1ef1c l\u00e0 g\u00ec? M\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n h\u1ecdc ph\u1ed5 bi\u1ebfn v\u1ec1 s\u1ed1 th\u1ef1c<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 h\u00ecnh t\u1ea1o b\u1edfi hai n\u1eeda m\u1eb7t ph\u1eb3ng c\u00f3 chung b\u1edd l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng d; s\u1ed1 \u0111o c\u1ee7a n\u00f3 b\u1eb1ng s\u1ed1 \u0111o g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n, t\u1ee9c g\u00f3c t\u1ea1o b\u1edfi hai tia c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi d t\u1ea1i m\u1ed9t \u0111i\u1ec3m v\u00e0 l\u1ea7n l\u01b0\u1ee3t n\u1eb1m trong hai n\u1eeda m\u1eb7t ph\u1eb3ng. S\u1ed1 \u0111o [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":622410,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"g\u00f3c nh\u1ecb di\u1ec7n","_yoast_wpseo_title":"G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00ec? C\u00e1ch x\u00e1c \u0111\u1ecbnh g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n","_yoast_wpseo_metadesc":"G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00ec? N\u1eafm \u0111\u1ecbnh ngh\u0129a, c\u00e1ch x\u00e1c \u0111\u1ecbnh g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n, ph\u00e2n bi\u1ec7t v\u1edbi g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng v\u00e0 luy\u1ec7n 4 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i ngay.","footnotes":""},"categories":[29235,3910,30453],"tags":[],"class_list":["post-620588","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-goc-to-mo","category-kham-pha","category-kien-thuc"],"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>G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00ec? C\u00e1ch x\u00e1c \u0111\u1ecbnh g\u00f3c ph\u1eb3ng nh\u1ecb di\u1ec7n<\/title>\n<meta name=\"description\" content=\"G\u00f3c nh\u1ecb di\u1ec7n l\u00e0 g\u00ec? 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