{"id":298366,"date":"2023-12-25T18:57:36","date_gmt":"2023-12-25T11:57:36","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=298366"},"modified":"2023-12-25T18:57:36","modified_gmt":"2023-12-25T11:57:36","slug":"truc-tam","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/truc-tam\/","title":{"rendered":"Tr\u1ef1c t\u00e2m l\u00e0 g\u00ec? X\u00e1c \u0111\u1ecbnh tr\u1ef1c t\u00e2m trong tam gi\u00e1c"},"content":{"rendered":"

Trong h\u00ecnh h\u1ecdc, tr\u1ef1c t\u00e2m l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng \u0111\u1ed1i v\u1edbi c\u00e1c tam gi\u00e1c nh\u1ecdn, t\u00f9, v\u00e0 vu\u00f4ng. \u0110\u00e2y l\u00e0 m\u1ed9t \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t n\u1eb1m trong tam gi\u00e1c, li\u00ean quan m\u1eadt thi\u1ebft \u0111\u1ebfn ba \u0111\u01b0\u1eddng cao. Lo\u1ea1i \u0111\u01b0\u1eddng n\u00e0y c\u00f2n mang \u0111\u1ebfn nhi\u1ec1u t\u00ednh ch\u1ea5t \u0111\u1ed9c \u0111\u00e1o v\u00e0 c\u00f3 \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau. B\u00e0i vi\u1ebft n\u00e0y s\u1ebd gi\u1edbi thi\u1ec7u chi ti\u1ebft v\u1ec1 m\u1ecdi th\u00f4ng tin li\u00ean quan \u0111\u1ebfn tr\u1ef1c t\u00e2m l\u00e0 g\u00ec. \u0110\u1ed3ng th\u1eddi, b\u00e0i vi\u1ebft s\u1ebd cung c\u1ea5p m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp v\u00ed d\u1ee5 \u0111\u1ec3 gi\u00fap ng\u01b0\u1eddi \u0111\u1ecdc hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1ch \u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c n\u00e0y trong th\u1ef1c t\u1ebf.<\/p>\n

Tr\u1ef1c t\u00e2m l\u00e0 g\u00ec?<\/h2>\n

Tr\u1ef1c t\u00e2m hay c\u00f2n th\u01b0\u1eddng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao. V\u1eady tr\u1ef1c t\u00e2m l\u00e0 g\u00ec? L\u00e0 tam gi\u00e1c c\u00f3 m\u1ed9t g\u00f3c vu\u00f4ng v\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u1ef1c t\u00e2m c\u1ee7a n\u00f3. Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao n\u00e0y l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i t\u1eeb trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u1edbi g\u00f3c vu\u00f4ng v\u1edbi tr\u1ecdng t\u00e2m tam gi\u00e1c. \u0110\u00e2y c\u0169ng l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng n\u1ed1i tr\u1ecdng t\u00e2m v\u00e0 \u0111\u1ec9nh \u0111\u1ed1i di\u1ec7n v\u1edbi g\u00f3c vu\u00f4ng.<\/p>\n

\u0110\u1ec3 x\u00e1c \u0111\u1ecbnh tr\u1ef1c t\u00e2m c\u1ee7a m\u1ed9t tam gi\u00e1c, ta ch\u1ec9 c\u1ea7n v\u1ebd ba \u0111\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 t\u00ecm \u0111i\u1ec3m giao c\u1ee7a ch\u00fang. N\u00f3 c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng nhi\u1ec1u c\u00e1ch kh\u00e1c nhau. Trong \u0111\u00f3 ph\u01b0\u01a1ng ph\u00e1p s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc l\u00e0 ph\u1ed5 bi\u1ebfn nh\u1ea5t.<\/p>\n

Tx = (x1 + x2 + x3)\/3 Ty = (y1 + y2 + y3)\/3<\/strong><\/p>\n

Trong \u0111\u00f3, (x1, y1), (x2, y2) v\u00e0 (x3, y3) l\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c, v\u00e0 Tx v\u00e0 Ty l\u1ea7n l\u01b0\u1ee3t l\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a tr\u1ef1c t\u00e2m.<\/p>\n

\"truc-tam-3.\"<\/picture><\/p>\n

Vai tr\u00f2 c\u1ee7a tr\u1ef1c t\u00e2m<\/h2>\n

Tr\u1ef1c t\u00e2m l\u00e0 m\u1ed9t \u0111i\u1ec3m quan tr\u1ecdng trong h\u00ecnh h\u1ecdc, v\u00e0 c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng trong l\u0129nh v\u1ef1c n\u00e0y. M\u1ed9t trong nh\u1eefng \u1ee9ng d\u1ee5ng quan tr\u1ecdng nh\u1ea5t c\u1ee7a tr\u1ef1c t\u00e2m l\u00e0 t\u00ednh to\u00e1n di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c. Di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c b\u1eb1ng m\u1ed9t n\u1eeda t\u00edch s\u1ed1 \u0111\u1ed9 d\u00e0i \u0111\u00e1y v\u00e0 chi\u1ec1u cao t\u01b0\u01a1ng \u1ee9ng v\u1edbi \u0111\u00e1y \u0111\u00f3. Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao l\u00e0m t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp c\u1ee7a tam gi\u00e1c, chi\u1ec1u cao t\u01b0\u01a1ng \u1ee9ng v\u1edbi \u0111\u00e1y \u0111\u00f3 ch\u00ednh l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb tr\u1ef1c t\u00e2m \u0111\u1ebfn \u0111\u00e1y. V\u00ec v\u1eady, ta c\u00f3 th\u1ec3 t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c nh\u01b0 sau:<\/p>\n

S = 1\/2 x AB x HC<\/strong><\/p>\n

Trong \u0111\u00f3, AB l\u00e0 \u0111\u1ed9 d\u00e0i \u0111\u00e1y c\u1ee7a tam gi\u00e1c v\u00e0 HC l\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb tr\u1ef1c t\u00e2m \u0111\u1ebfn \u0111\u00e1y AB.<\/p>\n

\"truc-tam-1\"<\/picture><\/p>\n

Ngo\u00e0i ra, giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao c\u00f2n c\u00f3 vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c x\u00e1c \u0111\u1ecbnh c\u00e1c \u0111\u01b0\u1eddng trung tr\u1ef1c v\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c. \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t c\u1ea1nh l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua tr\u1ef1c t\u00e2m v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh \u0111\u00f3. \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a m\u1ed9t c\u1ea1nh l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua t\u00e2m vu\u00f4ng g\u00f3c v\u00e0 gi\u1eefa \u0111i\u1ec3m \u0111\u1ea7u m\u00fat c\u1ee7a c\u1ea1nh \u0111\u00f3 v\u00e0 \u0111\u1ec9nh t\u01b0\u01a1ng \u1ee9ng v\u1edbi c\u1ea1nh \u0111\u00f3.<\/p>\n

T\u00ednh ch\u1ea5t tr\u1ef1c t\u00e2m<\/h2>\n

Tr\u1ef1c t\u00e2m c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 \u0111i\u1ec3m giao c\u1ee7a \u0111\u01b0\u1eddng trung tr\u1ef1c v\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong tam gi\u00e1c. N\u00f3 c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 \u0111i\u1ec3m m\u00e0 ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1eaft nhau.<\/p>\n

M\u1ed9t t\u00ednh ch\u1ea5t th\u00fa v\u1ecb kh\u00e1c c\u1ee7a tr\u1ef1c t\u00e2m l\u00e0 n\u00f3 c\u00e1ch c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c m\u1ed9t kho\u1ea3ng b\u1eb1ng nhau. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 n\u1ebfu ta \u0111o \u0111\u1ed9 d\u00e0i t\u1eeb giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao \u0111\u1ebfn m\u1ed7i \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c. Th\u00ec ch\u00fang s\u1ebd b\u1eb1ng nhau.<\/p>\n

\u0110\u01b0\u1eddng n\u00e0y c\u0169ng l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp c\u1ee7a tam gi\u00e1c, t\u1ee9c l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n l\u1edbn nh\u1ea5t m\u00e0 c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c qua ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c.<\/p>\n

\"truc-tam-2\"<\/picture><\/p>\n

Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c nh\u1ecdn n\u1eb1m b\u00ean trong tam gi\u00e1c. Trong khi \u0111\u00f3, giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c t\u00f9 n\u1eb1m b\u00ean ngo\u00e0i tam gi\u00e1c. \u0110i\u1ec1u n\u00e0y ph\u1ea3n \u00e1nh s\u1ef1 kh\u00e1c bi\u1ec7t trong v\u1ecb tr\u00ed c\u1ee7a tr\u1ef1c t\u00e2m \u0111\u1ed1i v\u1edbi c\u00e1c lo\u1ea1i tam gi\u00e1c kh\u00e1c nhau.<\/p>\n

N\u1ebfu l\u00e0 tam gi\u00e1c vu\u00f4ng, tr\u1ef1c t\u00e2m s\u1ebd n\u1eb1m tr\u00ean c\u1ea1nh huy\u1ec1n v\u00e0 ch\u00ednh gi\u1eefa hai \u0111\u1ec9nh vu\u00f4ng g\u00f3c c\u1ee7a tam gi\u00e1c.<\/p>\n

N\u1ebfu ta v\u1ebd c\u00e1c \u0111\u01b0\u1eddng t\u1eeb c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u1ebfn tr\u1ef1c t\u00e2m, ch\u00fang s\u1ebd c\u1eaft c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c th\u00e0nh c\u00e1c \u0111o\u1ea1n th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi c\u00e1c c\u1ea1nh \u0111\u00f3.<\/p>\n

Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c. N\u1ebfu ta bi\u1ebft \u0111\u1ed9 d\u00e0i c\u00e1c \u0111o\u1ea1n th\u1eb3ng t\u1eeb tr\u1ef1c t\u00e2m \u0111\u1ebfn c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c. Ta c\u00f3 th\u1ec3 t\u00ednh to\u00e1n \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c b\u1eb1ng \u0111\u1ecbnh l\u00fd Pythagoras ho\u1eb7c c\u00e1c c\u00f4ng th\u1ee9c h\u00ecnh h\u1ecdc kh\u00e1c.<\/p>\n

C\u00e1ch x\u00e1c \u0111\u1ecbnh tr\u1ef1c t\u00e2m<\/h2>\n

Tr\u1ef1c t\u00e2m l\u00e0 g\u00ec? C\u00e1ch x\u00e1c \u0111\u1ecbnh ra sao? \u0110\u1ecdc h\u1ebft m\u1ee5c n\u00e0y b\u1ea1n nh\u00e9.<\/p>\n

\u0110\u1ed1i v\u1edbi tam gi\u00e1c nh\u1ecdn, c\u00e2n, \u0111\u1ec1u<\/strong><\/p>\n

\u0110\u1ec3 x\u00e1c \u0111\u1ecbnh giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao n\u00e0y, ta c\u00f3 th\u1ec3 v\u1ebd hai \u0111\u01b0\u1eddng cao t\u1eeb hai \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c v\u00e0 n\u01a1i ch\u00fang c\u1eaft nhau ch\u00ednh l\u00e0 tr\u1ef1c t\u00e2m. Ho\u1eb7c ta c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb m\u1ed9t \u0111\u1ec9nh \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n. V\u00e0 v\u1ebd \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c t\u1eeb \u0111\u1ec9nh \u0111\u00f3 xu\u1ed1ng \u0111\u01b0\u1eddng trung tuy\u1ebfn. N\u01a1i hai \u0111\u01b0\u1eddng n\u00e0y c\u1eaft nhau ch\u00ednh l\u00e0 tr\u1ef1c t\u00e2m.<\/p>\n

\u0110\u1ed1i v\u1edbi tam gi\u00e1c t\u00f9<\/strong><\/p>\n

Tr\u1ef1c t\u00e2m n\u1eb1m b\u00ean ngo\u00e0i tam gi\u00e1c v\u00e0 g\u1ea7n trung \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u1ed1i \u0111\u1ec9nh. \u0110\u1ec3 x\u00e1c \u0111\u1ecbnh tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c t\u00f9, ta c\u0169ng v\u1ebd hai \u0111\u01b0\u1eddng cao t\u1eeb hai \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c. Nh\u01b0ng ta c\u1ea7n v\u1ebd th\u00eam m\u1ed9t \u0111\u01b0\u1eddng cao t\u1eeb \u0111\u1ec9nh g\u00f3c t\u00f9 xu\u1ed1ng c\u1ea1nh \u0111\u1ed1i di\u1ec7n. Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao l\u00e0 n\u01a1i m\u00e0 \u0111\u01b0\u1eddng cao m\u1edbi c\u1eaft \u0111\u01b0\u1eddng cao kh\u00e1c. N\u00f3 n\u1eb1m ngo\u00e0i mi\u1ec1n tam gi\u00e1c \u0111\u00f3 v\u00e0 g\u1ea7n trung \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u1ed1i \u0111\u1ec9nh.<\/p>\n

\u0110\u1ed1i v\u1edbi tam gi\u00e1c vu\u00f4ng<\/strong><\/p>\n

Tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c vu\u00f4ng tr\u00f9ng v\u1edbi \u0111\u1ec9nh c\u1ee7a g\u00f3c vu\u00f4ng. \u0110i\u1ec1u n\u00e0y xu\u1ea5t ph\u00e1t t\u1eeb vi\u1ec7c hai c\u1ea1nh t\u1ea1o th\u00e0nh g\u00f3c vu\u00f4ng c\u0169ng l\u00e0 \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c. Do \u0111\u00f3, kh\u00f4ng c\u1ea7n v\u1ebd th\u00eam \u0111\u01b0\u1eddng cao hay t\u00ecm \u0111i\u1ec3m giao kh\u00e1c, t\u00e2m n\u00e0y ch\u00ednh l\u00e0 \u0111\u1ec9nh g\u00f3c vu\u00f4ng.<\/p>\n

Tr\u1ef1c t\u00e2m l\u00e0 m\u1ed9t \u0111i\u1ec3m r\u1ea5t quan tr\u1ecdng v\u00ec n\u00f3 l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c. \u0110\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n \u0111i qua ba \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c v\u00e0 c\u00f3 t\u00e2m l\u00e0 tr\u1ef1c t\u00e2m. N\u00f3 c\u0169ng l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n \u1ee9ng v\u1edbi tam gi\u00e1c \u0111\u1ed1i ngh\u1ecbch.<\/p>\n

Vi\u1ec7c x\u00e1c \u0111\u1ecbnh giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao c\u00f2n c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn tam gi\u00e1c. V\u00ed d\u1ee5 nh\u01b0 t\u00ecm t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp, t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp, t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n \u0111\u1ed1i ngh\u1ecbch, t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp v\u00e0 n\u1eeda \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp.<\/p>\n

\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a tr\u1ef1c t\u00e2m<\/h2>\n

Sau khi hi\u1ec3u \u0111\u01b0\u1ee3c tr\u1ef1c t\u00e2m l\u00e0 g\u00ec. Ch\u00fang ta s\u1ebd \u0111i \u0111\u1ebfn ph\u1ea7n \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a tr\u1ef1c t\u00e2m xem n\u00f3 c\u00f3 \u00edch nh\u01b0 th\u1ebf n\u00e0o nh\u00e9.<\/p>\n

Ki\u1ebfn tr\u00fac v\u00e0 x\u00e2y d\u1ef1ng<\/h3>\n

Vi\u1ec7c c\u00f3 tr\u1ee5 c\u1ed9t \u0111\u1eb7t t\u1ea1i v\u1ecb tr\u00ed \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh th\u00f4ng qua tr\u1ef1c t\u00e2m gi\u00fap t\u0103ng kh\u1ea3 n\u0103ng ch\u1ecbu t\u1ea3i c\u1ee7a c\u00f4ng tr\u00ecnh. Tr\u1ecdng l\u1ef1c t\u1eeb c\u00e1c ph\u1ea7n tr\u00ean cao c\u1ee7a c\u00f4ng tr\u00ecnh \u0111\u01b0\u1ee3c truy\u1ec1n xu\u1ed1ng \u0111\u00e1ng k\u1ec3 th\u00f4ng qua tr\u1ee5 c\u1ed9t h\u1ed7 tr\u1ee3. V\u00e0 vi\u1ec7c \u0111\u1eb7t ch\u00fang t\u1ea1i v\u1ecb tr\u00ed chi\u1ebfn l\u01b0\u1ee3c gi\u00fap gi\u1ea3m nguy c\u01a1 \u0111\u1ed5 s\u1eadp.<\/p>\n

\"truc-tam-6\"<\/picture><\/p>\n

Quy ho\u1ea1ch \u0111\u00f4 th\u1ecb<\/h3>\n

Tr\u1ef1c t\u00e2m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh trung t\u00e2m c\u1ee7a khu v\u1ef1c c\u1ed9ng \u0111\u1ed3ng ho\u1eb7c th\u00e0nh ph\u1ed1, v\u00e0 t\u1eeb \u0111\u00f3, quy ho\u1ea1ch vi\u00ean c\u00f3 th\u1ec3 \u0111\u01b0a ra quy\u1ebft \u0111\u1ecbnh v\u1ec1 v\u1ecb tr\u00ed l\u1eafp \u0111\u1eb7t c\u00e1c tr\u1ea1m ph\u1ee5c v\u1ee5 nh\u01b0 b\u1ec7nh vi\u1ec7n, tr\u01b0\u1eddng h\u1ecdc, c\u00f4ng vi\u00ean, hay c\u00e1c c\u01a1 s\u1edf c\u00f4ng c\u1ed9ng kh\u00e1c. Vi\u1ec7c t\u1eadp trung c\u00e1c d\u1ecbch v\u1ee5 n\u00e0y quanh m\u1ed9t tr\u1ef1c t\u00e2m c\u00f3 th\u1ec3 gi\u00fap t\u1ed1i \u01b0u h\u00f3a ti\u1ec7n \u00edch v\u00e0 thu\u1eadn ti\u1ec7n cho c\u01b0 d\u00e2n \u0111\u1ecba ph\u01b0\u01a1ng.<\/p>\n

\"\"<\/picture><\/p>\n

Quy ho\u1ea1ch \u0111\u00f4 th\u1ecb c\u00f3 s\u1ef1 t\u00edch h\u1ee3p gi\u1eefa giao \u0111i\u1ec3m n\u00e0y c\u00f3 th\u1ec3 g\u00f3p ph\u1ea7n v\u00e0o vi\u1ec7c x\u00e2y d\u1ef1ng th\u00e0nh ph\u1ed1 th\u00f4ng minh. C\u00e1c d\u1eef li\u1ec7u v\u1ecb tr\u00ed \u0111\u01b0\u1ee3c thu th\u1eadp t\u1eeb tr\u1ef1c t\u00e2m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c k\u1ebft h\u1ee3p v\u1edbi c\u00f4ng ngh\u1ec7 th\u00f4ng tin \u0111\u1ec3 c\u1ea3i thi\u1ec7n qu\u1ea3n l\u00fd giao th\u00f4ng, d\u1ecbch v\u1ee5 c\u00f4ng c\u1ed9ng v\u00e0 an ninh, t\u1ea1o ra m\u1ed9t m\u00f4i tr\u01b0\u1eddng s\u1ed1ng hi\u1ec7u qu\u1ea3 v\u00e0 ti\u1ec7n nghi.<\/p>\n

Nghi\u00ean c\u1ee9u \u0111\u1ea5t \u0111ai<\/h3>\n

Trong l\u0129nh v\u1ef1c nghi\u00ean c\u1ee9u \u0111\u1ea5t \u0111ai, vi\u1ec7c x\u00e1c \u0111\u1ecbnh tr\u1ef1c t\u00e2m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c th\u1ef1c hi\u1ec7n th\u00f4ng qua c\u00e1c ph\u01b0\u01a1ng ph\u00e1p \u0111o l\u01b0\u1eddng ch\u00ednh x\u00e1c. Nh\u01b0 to\u00e0n b\u1ed9 GPS (Global Positioning System), thi\u1ebft b\u1ecb \u0111\u1ecbnh v\u1ecb v\u1ec7 tinh,… Ho\u1eb7c c\u00e1c k\u1ef9 thu\u1eadt \u0111o l\u01b0\u1eddng \u0111\u1ecba l\u00fd ch\u00ednh x\u00e1c kh\u00e1c. M\u1ed9t khi \u0111\u00e3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c, c\u00e1c tr\u1ea1m \u0111o \u0111\u1ea5t \u0111ai s\u1ebd \u0111\u01b0\u1ee3c \u0111\u1eb7t xung quanh \u0111i\u1ec3m n\u00e0y \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o r\u1eb1ng c\u00e1c d\u1eef li\u1ec7u thu th\u1eadp \u0111\u01b0\u1ee3c l\u00e0 \u0111\u1ea1i di\u1ec7n cho to\u00e0n b\u1ed9 khu v\u1ef1c quan t\u00e2m.<\/p>\n

H\u1ec7 th\u1ed1ng \u0111i\u1ec1u khi\u1ec3n Robot<\/h3>\n

Th\u01b0\u1eddng \u0111\u01b0\u1ee3c t\u00edch h\u1ee3p v\u1edbi h\u1ec7 th\u1ed1ng \u0111o l\u01b0\u1eddng, nh\u01b0 c\u00e1c c\u1ea3m bi\u1ebfn v\u1ecb tr\u00ed, h\u1ec7 th\u1ed1ng GPS, ho\u1eb7c c\u00e1c thi\u1ebft b\u1ecb \u0111o l\u01b0\u1eddng v\u1ecb tr\u00ed v\u1ec7 tinh kh\u00e1c. \u0110i\u1ec1u n\u00e0y gi\u00fap x\u00e1c \u0111\u1ecbnh m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u1ecb tr\u00ed tuy\u1ec7t \u0111\u1ed1i c\u1ee7a robot trong kh\u00f4ng gian to\u00e0n c\u1ea7u. C\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u1ed1i t\u00e2m n\u00e0y v\u1edbi c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c cung c\u1ea5p m\u1ed9t c\u01a1 s\u1edf h\u00ecnh h\u1ecdc m\u1ea1nh m\u1ebd \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a robot trong m\u00f4i tr\u01b0\u1eddng c\u1ee5 th\u1ec3.<\/p>\n

\"\"<\/picture><\/p>\n

Gi\u00e1o d\u1ee5c h\u00ecnh h\u1ecdc<\/h3>\n

Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng cao l\u00e0 m\u1ed9t v\u00ed d\u1ee5 th\u1ef1c t\u1ebf gi\u00e1o d\u1ee5c trong vi\u1ec7c gi\u1ea3ng d\u1ea1y h\u00ecnh h\u1ecdc. N\u00f3 gi\u00fap h\u1ecdc sinh hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1c \u0111\u1eb7c t\u00ednh v\u00e0 t\u00ednh ch\u1ea5t. T\u1eeb \u0111\u00f3 ph\u00e1t tri\u1ec3n k\u1ef9 n\u0103ng gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 v\u00e0 t\u01b0 duy h\u00ecnh h\u1ecdc.<\/p>\n

\u1ee8ng d\u1ee5ng trong c\u00f4ng nghi\u1ec7p v\u00e0 c\u00f4ng ngh\u1ec7<\/h3>\n

Trong m\u00f4i tr\u01b0\u1eddng c\u00f4ng nghi\u1ec7p, quy tr\u00ecnh gi\u00e1m s\u00e1t t\u1eeb xa \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o an to\u00e0n v\u00e0 hi\u1ec7u su\u1ea5t. S\u1eed d\u1ee5ng tr\u1ef1c t\u00e2m gi\u00fap x\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed c\u1ee7a c\u00e1c thi\u1ebft b\u1ecb v\u00e0 nh\u00e2n vi\u00ean. \u0110\u1ed3ng th\u1eddi cung c\u1ea5p d\u1eef li\u1ec7u ch\u00ednh x\u00e1c cho c\u00e1c h\u1ec7 th\u1ed1ng gi\u00e1m s\u00e1t t\u1eeb xa. \u0110i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng trong c\u00e1c nh\u00e0 m\u00e1y s\u1ea3n xu\u1ea5t, khu v\u1ef1c l\u01b0u kho, v\u00e0 c\u00e1c m\u00f4i tr\u01b0\u1eddng c\u00f4ng nghi\u1ec7p kh\u00e1c.<\/p>\n

M\u1ed9t s\u1ed1 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i d\u1ec5 hi\u1ec3u v\u1ec1 tr\u1ef1c t\u00e2m<\/h2>\n

B\u00e0i t\u1eadp 1:<\/strong> Cho tam gi\u00e1c vu\u00f4ng ABC c\u00f3 tr\u1ef1c t\u00e2m H. Bi\u1ebft AB = 3, AC = 4 v\u00e0 BC = 5. T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n AH.<\/p>\n

\"truc-tam-8\"<\/picture><\/p>\n

Gi\u1ea3i:<\/strong><\/p>\n

Ta c\u00f3: AH = 2.HN (v\u1edbi N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC)<\/p>\n

V\u00ec tam gi\u00e1c ABC c\u00f3 tr\u1ef1c t\u00e2m H n\u00ean ta c\u00f3:<\/p>\n

BN = CN = a<\/p>\n

AH = 2.HN = 2.(BC\/2 – a) = BC – 2a<\/p>\n

\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pythagore trong tam gi\u00e1c vu\u00f4ng ABC:<\/p>\n

BC^2 = AB^2 + AC^2<\/p>\n

5^2 = 3^2 + 4^2<\/p>\n

25 = 9 + 16<\/p>\n

a^2 = 25\/4<\/p>\n

a = 5\/2<\/p>\n

V\u1eady:<\/p>\n

AH = BC – 2a = 5 – 2.5\/2 = 5\/2<\/p>\n

B\u00e0i t\u1eadp 2<\/strong>: Cho tam gi\u00e1c ABC c\u00f3 tr\u1ef1c t\u00e2m H. Bi\u1ebft AB = 8, AC = 10 v\u00e0 BC = 12. T\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c ABC.<\/p>\n

\"truc-tam-9\"<\/picture><\/p>\n

Gi\u1ea3i:<\/strong><\/p>\n

V\u00ec tam gi\u00e1c ABC c\u00f3 tr\u1ef1c t\u00e2m H n\u00ean ta c\u00f3:<\/p>\n

HN = (BN + CN)\/2 = BC\/2<\/p>\n

\u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch tam gi\u00e1c:<\/p>\n

S = 1\/2 . AB . AC . sin(A)<\/p>\n

V\u1edbi A l\u00e0 g\u00f3c gi\u1eefa AB v\u00e0 AC.<\/p>\n

Ta c\u00f3 th\u1ec3 t\u00ednh sin(A) b\u1eb1ng c\u00e1ch \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd cosin trong tam gi\u00e1c ABC:<\/p>\n

BC^2 = AB^2 + AC^2 – 2AB.AC.cos(A)<\/p>\n

12^2 = 8^2 + 10^2 – 2.8.10.cos(A)<\/p>\n

144 = 164 – 160cos(A)<\/p>\n

cos(A) = 5\/8<\/p>\n

sin(A) = \u221a(1 – cos^2(A)) = \u221a(1 – 25\/64) = \u221a(39\/64)<\/p>\n

V\u1eady:<\/p>\n

S = 1\/2 . AB . AC . sin(A) = 1\/2 . 8 . 10 . \u221a(39\/64) = 20\u221a39\/4<\/p>\n

B\u00e0i t\u1eadp 3<\/strong>: Cho tam gi\u00e1c ABC c\u00f3 tr\u1ef1c t\u00e2m H. Bi\u1ebft AB = 7, AC = 9 v\u00e0 AH = 4. T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n BH.<\/p>\n

\"truc-tam-10\"<\/picture><\/p>\n

Gi\u1ea3i:<\/strong><\/p>\n

V\u00ec tam gi\u00e1c ABC c\u00f3 tr\u1ef1c t\u00e2m H n\u00ean ta c\u00f3:<\/p>\n

AH = 2.HN (v\u1edbi N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC)<\/p>\n

V\u1eady:<\/p>\n

HN = AH\/2 = 2<\/p>\n

\u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pythagore trong tam gi\u00e1c vu\u00f4ng ABH:<\/p>\n

BH^2 = AH^2 + AB^2\/4<\/p>\n

BH^2 = 4^2 + 7^2\/4<\/p>\n

BH^2 = 16 + 49\/4<\/p>\n

BH = \u221a(16 + 49\/4) = \u221a(113)\/2<\/p>\n

K\u1ebft lu\u1eadn<\/h2>\n

Tr\u1ef1c t\u00e2m l\u00e0 \u0111i\u1ec3m giao c\u1ee7a ba \u0111\u01b0\u1eddng cao. N\u00f3 li\u00ean quan m\u1eadt thi\u1ebft \u0111\u1ebfn c\u1ea5u tr\u00fac tam gi\u00e1c v\u00e0 mang \u0111\u1ebfn nhi\u1ec1u t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t. B\u00e0i vi\u1ebft tr\u00ean \u0111\u00e3 tr\u00ecnh b\u00e0y chi ti\u1ebft v\u1ec1 tr\u1ef1c t\u00e2m. Qua b\u00e0i vi\u1ebft tr\u1ef1c t\u00e2m l\u00e0 g\u00ec<\/em> ng\u01b0\u1eddi \u0111\u1ecdc c\u00f3 th\u1ec3 hi\u1ec3u \u0111\u01b0\u1ee3c kh\u00e1i ni\u1ec7m c\u1ee7a n\u00f3 c\u0169ng nh\u01b0 c\u00e1ch x\u00e1c \u0111\u1ecbnh v\u00e0 t\u00ednh to\u00e1n t\u1ecda \u0111\u1ed9 th\u00f4ng qua c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc.<\/p>\n

Ngo\u00e0i ra, n\u00f3 c\u00f2n c\u00f3 \u1ee9ng d\u1ee5ng trong ki\u1ebfn tr\u00fac, quy ho\u1ea1ch \u0111\u00f4 th\u1ecb, nghi\u00ean c\u1ee9u \u0111\u1ea5t \u0111ai, h\u1ec7 th\u1ed1ng \u0111i\u1ec1u khi\u1ec3n robot,… Hay th\u1eadm ch\u00ed l\u00e0 gi\u00e1o d\u1ee5c h\u00ecnh h\u1ecdc v\u00e0 c\u00e1c \u1ee9ng d\u1ee5ng c\u00f4ng nghi\u1ec7p kh\u00e1c. Th\u00f4ng qua vi\u1ec7c t\u00ecm hi\u1ec3u v\u1ec1 tr\u1ef1c t\u00e2m, \u0111\u1ed9c gi\u1ea3 c\u00f3 th\u1ec3 n\u1eafm b\u1eaft \u0111\u01b0\u1ee3c s\u1ef1 quan tr\u1ecdng c\u1ee7a n\u00f3 trong l\u0129nh v\u1ef1c h\u00ecnh h\u1ecdc v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf.<\/p>\n

\u0110\u1eebng qu\u00ean theo d\u00f5i Ho\u00e0ng H\u00e0 Mobile \u0111\u1ec3 kh\u00f4ng b\u1ecf l\u1ee1 b\u1ea5t k\u1ef3 tin t\u1ee9c hot n\u00e0o b\u1ea1n nh\u00e9. M\u1ecdi th\u00f4ng b\u00e1o v\u1ec1 c\u00e1c s\u1ea3n ph\u1ea9m m\u1edbi, c\u00e1c khuy\u1ebfn m\u00e3i h\u1ea5p d\u1eabn, \u0111\u1ed9c \u0111\u00e1o ch\u1ec9 c\u00f3 t\u1ea1i Ho\u00e0ng H\u00e0 Mobile.<\/p>\n

Xem th\u00eam:<\/strong><\/p>\n