Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
\u0110\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp l\u00e0 hai kh\u00e1i ni\u1ec7m ri\u00eang bi\u1ec7t c\u1ea7n ph\u1ea3i n\u1eafm r\u00f5 \u0111\u1ec3 tr\u00e1nh b\u1ecb nh\u1ea7m l\u1eabn. Ch\u00ednh v\u00ec v\u1eady b\u00e0i gi\u1ea3ng sau, https::\/\/toppy.vn\/ s\u1ebd gi\u00fap c\u00e1c em h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c c\u0169ng nh\u01b0 \u00f4n t\u1eadp l\u1ea1i nh\u1eefng b\u00e0i t\u1eadp t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn l\u1edbp 9 \u0111\u1ec3 \u1ee9ng d\u1ee5ng gi\u1ea3i \u0111\u01b0\u1ee3c hi\u1ec7u qu\u1ea3 nh\u1ea5t.<\/p>\n\n\n\n
I. L\u00fd thuy\u1ebft \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp:<\/p>\n\n\n\n
\u0110\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp:<\/p>\n\n\n\n
Trong h\u00ecnh h\u1ecdc, \u0111\u01b0\u1eddng tr\u00f2n m\u00e0 \u0111i qua t\u1ea5t c\u1ea3 nh\u1eefng \u0111\u1ec9nh c\u1ee7a 1 \u0111a gi\u00e1c l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp c\u1ee7a \u0111a gi\u00e1c \u0111\u00f3. \u0110a gi\u00e1c n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111a gi\u00e1c n\u1ed9i ti\u1ebfp c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n\n\n\n
\u0110\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp:<\/p>\n\n\n\n
\u0110\u01b0\u1eddng tr\u00f2n m\u00e0 ti\u1ebfp x\u00fac t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh c\u1ee7a \u0111a gi\u00e1c l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp \u0111a gi\u00e1c. \u0110a gi\u00e1c n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111a gi\u00e1c ngo\u1ea1i ti\u1ebfp c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n. \u0110\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n l\u1edbn nh\u1ea5t m\u00e0 n\u1eb1m trong tam gi\u00e1c \u0111\u00f3. \u0110\u1ed1i v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c, t\u00e2m c\u1ee7a n\u00f3 l\u00e0 giao \u0111i\u1ec3m 3 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong.<\/p>\n\n\n\n
Kh\u00e1i ni\u1ec7m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp ngo\u1ea1i ti\u1ebfp v\u00e0 b\u00e0ng ti\u1ebfp c\u1ee7a tam gi\u00e1c<\/p>\n\n\n\n
\u0110\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp:<\/p>\n\n\n\n
B\u00ean c\u1ea1nh kh\u00e1i ni\u1ec7m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp v\u00e0 n\u1ed9i ti\u1ebfp c\u00f2n c\u00f3 kh\u00e1i ni\u1ec7m v\u1ec1 \u0111\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp l\u1edbp 9. Theo \u0111\u00f3, \u0111\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n n\u1eb1m ngo\u00e0i c\u1ee7a tam gi\u00e1c v\u00e0 ti\u1ebfp x\u00fac v\u1edbi 1 c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u00f3 v\u00e0 ti\u1ebfp x\u00fac v\u1edbi ph\u1ea7n k\u00e9o d\u00e0i c\u1ee7a 2 c\u1ea1nh c\u00f2n l\u1ea1i. T\u1ea5t c\u1ea3 m\u1ecdi tam gi\u00e1c \u0111\u1ec1u s\u1ebd c\u00f3 3 \u0111\u01b0\u1eddng tr\u00f2n ph\u00e2n bi\u1ec7t b\u00e0ng ti\u1ebfp v\u00e0 m\u1ed7i c\u00e1i s\u1ebd ti\u1ebfp x\u00fac v\u1edbi m\u1ed7i c\u1ea1nh c\u1ee7a tam gi\u00e1c.<\/p>\n\n\n\n
T\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp tam gi\u00e1c ch\u00ednh l\u00e0 giao \u0111i\u1ec3m \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong c\u1ee7a 1 g\u00f3c v\u1edbi nh\u1eefng \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c ngo\u00e0i \u0111\u1ed1i v\u1edbi 2 g\u00f3c c\u00f2n l\u1ea1i.<\/p>\n\n\n\n
B\u1ea5t k\u1ef3 c\u00e1c \u0111a gi\u00e1c \u0111\u1ec1u n\u00e0o c\u0169ng ch\u1ec9 c\u00f3 1 v\u00e0 ch\u1ec9 1 \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp, \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp.<\/p>\n\n\n\n
T\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp s\u1ebd tr\u00f9ng v\u1edbi t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp v\u00e0 ch\u00ednh l\u00e0 t\u00e2m c\u1ee7a \u0111a gi\u00e1c \u0111\u1ec1u.<\/p>\n\n\n\n
Cho \u0111a gi\u00e1c \u0111\u1ec1u c\u00f3 n c\u1ea1nh, a l\u00e0 \u0111\u1ed9 d\u00e0i m\u1ed7i c\u1ea1nh, r v\u00e0 R l\u1ea7n l\u01b0\u1ee3t l\u00e0 b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp v\u00e0 ngo\u1ea1i ti\u1ebfp c\u1ee7a \u0111a gi\u00e1c. Khi \u0111\u00f3 ta c\u00f3 c\u00f4ng th\u1ee9c t\u00ednh b\u00e1n k\u00ednh c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp v\u00e0 n\u1ed9i ti\u1ebfp nh\u01b0 sau:<\/p>\n\n\n\n
\u0110\u1ec3 \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c tr\u00ean m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c nh\u1ea5t, h\u00e3y c\u00f9ng \u00f4n t\u1eadp l\u1ea1i t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn l\u1edbp 9 ngay sau \u0111\u00e2y:<\/p>\n\n\n\n
Sin \u03b1 = C\u1ea1nh \u0111\u1ed1i\/C\u1ea1nh huy\u1ec1n<\/p>\n\n\n\n
Cos \u03b1 = C\u1ea1nh k\u1ec1\/C\u1ea1nh huy\u1ec1n<\/p>\n\n\n\n
Tan \u03b1 = C\u1ea1nh \u0111\u1ed1i\/C\u1ea1nh k\u1ec1<\/p>\n\n\n\n
Cot \u03b1 = C\u1ea1nh k\u1ec1\/C\u1ea1nh \u0111\u1ed1i<\/p>\n\n\n\n
C\u00f4ng th\u1ee9c t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn l\u1edbp 9<\/p>\n\n\n\n
\u0110\u00e2y l\u00e0 c\u00f4ng th\u1ee9c t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c l\u1edbp 9 c\u1ea7n ph\u1ea3i n\u1eafm v\u1eefng. Ngo\u00e0i ra \u0111\u1ec3 c\u00f3 th\u1ec3 gi\u1ea3i b\u00e0i t\u1eadp t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn, c\u00f4ng th\u1ee9c tr\u00ean c\u00f2n c\u00f3 th\u1ec3 nh\u1edb d\u1ec5 d\u00e0ng h\u01a1n qua c\u00e2u sau: Sin b\u1eb1ng \u0111\u1ed1i chia huy\u1ec1n, cos b\u1eb1ng k\u1ec1 chia huy\u1ec1n, tan b\u1eb1ng \u0111\u1ed1i chia k\u1ec1, cot b\u1eb1ng k\u1ec1 chia \u0111\u1ed1i.<\/p>\n\n\n\n
\u0110\u1ec3 c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh v\u00e0 v\u1ebd \u0111\u01b0\u1ee3c t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp v\u00e0 n\u1ed9i ti\u1ebfp c\u1ee7a tam gi\u00e1c c\u1ea7n ghi nh\u1edb \u0111\u01b0\u1ee3c l\u00fd thuy\u1ebft sau:<\/p>\n\n\n\n
Giao \u0111i\u1ec3m 3 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c.<\/p>\n\n\n\n
Giao \u0111i\u1ec3m 3 \u0111\u01b0\u1eddng trung tr\u1ef1c l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c.<\/p>\n\n\n\n
II. B\u00e0i t\u1eadp to\u00e1n 9 b\u00e0i \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp v\u00e0 n\u1ed9i ti\u1ebfp c\u1ee7a tam gi\u00e1c<\/p>\n\n\n\n
\u0110\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp, n\u1ed9i ti\u1ebfp l\u00e0 2 kh\u00e1i ni\u1ec7m v\u00f4 c\u00f9ng quan tr\u1ecdng v\u00e0 ph\u1ea3i ph\u00e2n bi\u1ec7t r\u00f5 r\u00e0ng \u0111\u1ec3 c\u00f3 th\u1ec3 v\u1eadn d\u1ee5ng \u0111\u01b0\u1ee3c ch\u00ednh x\u00e1c nh\u1ea5t. Ch\u00ednh v\u00ec v\u1eady d\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i gi\u1ea3i b\u00e0i t\u1eadp to\u00e1n 9 b\u00e0i \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp gi\u00fap c\u00e1c em ph\u00e2n bi\u1ec7t \u0111\u01b0\u1ee3c r\u00f5 r\u00e0ng nh\u1ea5t.<\/p>\n\n\n\n
B\u00e0i t\u1eadp 1 (B\u00e0i 63\/SGK trang 92, To\u00e1n 9, T\u1eadp 2):<\/p>\n\n\n\n
V\u1ebd tam gi\u00e1c ABC \u0111\u1ec1u v\u1edbi c\u1ea1nh a l\u00e0 3cm.<\/p>\n\n\n\n
V\u1ebd ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O, b\u00e1n k\u00ednh R ngo\u1ea1i ti\u1ebfp v\u1edbi tam gi\u00e1c ABC v\u00e0 t\u00ednh R.<\/p>\n\n\n\n
V\u1ebd ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O, b\u00e1n k\u00ednh r n\u1ed9i ti\u1ebfp v\u1edbi tam gi\u00e1c ABC v\u00e0 t\u00ednh r.<\/p>\n\n\n\n
V\u1ebd ti\u1ebfp tam gi\u00e1c IJK \u0111\u1ec1u v\u00e0 ngo\u1ea1i ti\u1ebfp v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n (O; R).<\/p>\n\n\n\n
B\u00e0i t\u1eadp to\u00e1n 9 b\u00e0i \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp, \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp c\u1ee7a tam gi\u00e1c<\/p>\n\n\n\n
B\u00e0i t\u1eadp 2 (B\u00e0i 63\/SGK trang 92, To\u00e1n 9, T\u1eadp 2)<\/p>\n\n\n\n
V\u1ebd h\u00ecnh tam gi\u00e1c \u0111\u1ec1u, h\u00ecnh l\u1ee5c gi\u00e1c \u0111\u1ec1u, h\u00ecnh vu\u00f4ng c\u00f9ng n\u1ed9i ti\u1ebfp trong \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O, b\u00e1n k\u00ednh R (O,R) sau \u0111\u00f3 t\u00ednh c\u00e1c c\u1ea1nh c\u1ee7a nh\u1eefng h\u00ecnh n\u00e0y theo R.<\/p>\n\n\n\n
B\u00e0i gi\u1ea3ng tr\u00ean \u0111\u00e3 cung c\u1ea5p l\u00fd thuy\u1ebft v\u1ec1 \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp c\u0169ng nh\u01b0 \u00f4n t\u1eadp l\u1ea1i ki\u1ebfn th\u1ee9c v\u1ec1 c\u00f4ng th\u1ee9c t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c l\u1edbp 9 \u0111\u1ec3 gi\u1ea3i nh\u1eefng b\u00e0i t\u1eadp li\u00ean quan. Hy v\u1ecdng \u0111\u00e2y s\u1ebd l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c b\u1ed5 \u00edch gi\u00fap c\u00e1c em h\u1ecdc sinh<\/a> \u00f4n t\u1eadp \u0111\u01b0\u1ee3c hi\u1ec7u qu\u1ea3. N\u1ebfu c\u00f3 nhu c\u1ea7u t\u00ecm ki\u1ebfm th\u00eam th\u00f4ng tin, c\u00e1c d\u1ea1ng to\u00e1n li\u00ean quan ho\u1eb7c c\u00f3 b\u1ea5t k\u1ef3 c\u00e2u h\u1ecfi n\u00e0o h\u00e3y truy c\u1eadp https::\/\/toppy.vn\/ \u0111\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i \u0111\u00e1p nhanh nh\u1ea5t c\u00f3 th\u1ec3.<\/p>\n\n\n\n <\/p>\n\n\n\n T\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp<\/p>\n\n\n\n Cung ch\u1ee9a g\u00f3c<\/p>\n\n\n\n T\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau \u2013 H\u1ecdc h\u00ecnh l\u1edbp 9 c\u00f9ng Vietlearn<\/p>\n\n\n\n V\u1ecb<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn \u0110\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp l\u00e0 hai kh\u00e1i ni\u1ec7m ri\u00eang bi\u1ec7t c\u1ea7n ph\u1ea3i n\u1eafm r\u00f5 \u0111\u1ec3 tr\u00e1nh b\u1ecb nh\u1ea7m l\u1eabn. Ch\u00ednh v\u00ec v\u1eady b\u00e0i gi\u1ea3ng sau, https::\/\/toppy.vn\/ s\u1ebd gi\u00fap c\u00e1c em h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c c\u0169ng nh\u01b0 \u00f4n t\u1eadp l\u1ea1i nh\u1eefng b\u00e0i t\u1eadp t\u1ec9 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9],"tags":[],"class_list":["post-985","post","type-post","status-publish","format-standard","hentry","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/985","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=985"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/985\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=985"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=985"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=985"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}