{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["7,32"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Trong tam gi\u00e1c $ABC$ c\u00f3 $\\,\\widehat{ABC}={{50}^{o}};\\widehat{ACB}={{32}^{o}}$. $H$ l\u00e0 ch\u00e2n \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c k\u1ebb t\u1eeb $A$ \u0111\u1ebfn $BC, AH= 3 \\,cm$. \u0110\u1ed9 d\u00e0i c\u1ea1nh $BC$ $\\approx $_input_ $(cm)$<br\/>(K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai)<\/span> ","hint":"T\u00ednh $CH$ v\u00e0 $BH$. ","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D22.png' \/><\/center><br\/>X\u00e9t $\\Delta AHB$ vu\u00f4ng t\u1ea1i $H$ ta c\u00f3: <br\/>$BH=AH.cotg \\widehat{ABC}$ <br\/> $\\Rightarrow BH =3.cotg {{50}^{o}}\\approx 2,52\\left( cm \\right)$ <br\/>X\u00e9t $\\Delta ACH$ vu\u00f4ng t\u1ea1i $H$ ta c\u00f3:<br\/> $HC=AH.cotg \\widehat{ACB}$ (h\u1ec7 th\u1ee9c v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow HC=3.cotg 32^o \\approx 4,8\\left( cm \\right)$<br\/>Suy ra: $BC=CH+HB \\approx 2,52+4,8=7,32\\,(\\,cm)$ <br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $7,32$<\/span><\/span><\/span>"}]}],"id_ques":1341},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$. K\u1ebb \u0111\u01b0\u1eddng cao $AH$. Bi\u1ebft $AC= 10 cm$, $\\widehat{B}=25^{o}$. \u0110\u1ed9 d\u00e0i c\u1ea1nh $AH$ x\u1ea5p x\u1ec9 b\u1eb1ng: ","select":["A. $8,3 cm$","B. $9,1 cm$","C. $9,5 cm$","D. $8,6 cm$"],"hint":"T\u00ednh g\u00f3c $C$, t\u1eeb \u0111\u00f3 \u00e1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean h\u1ec7 v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c \u0111\u1ec3 t\u00ednh $AH$.","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D17.png' \/><\/center><br\/><span class='basic_left'>X\u00e9t $\\Delta ABC$ c\u00f3: $\\widehat{A}=90^{o}$<br\/>$ \\widehat{C}=90^{o}-\\widehat{B}=90^{o}-25^{o}=65^{o}$<br\/>X\u00e9t $ \\Delta AHC$ c\u00f3: $\\widehat{H}=90^{o}$. Ta c\u00f3: <br\/>$AH= AC.sin \\widehat{C}$ (h\u1ec7 th\u1ee9c v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AH = 10.sin 65^{o}\\approx9,1\\, cm$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":4}]}],"id_ques":1342},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$.","select":["A. $AB= AC.sin B$","B. $AC= AB.cos B$","C. $AC= AB.cotg C$","D. $AC= AB.tg C$"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D13.png' \/><\/center><br\/> C\u00e2u A sai, v\u00ec nh\u1ea7m c\u00f4ng th\u1ee9c $AB= BC.sin C= BC.cos B$<br\/>C\u00e2u B sai, v\u00ec nh\u1ea7m c\u00f4ng th\u1ee9c $AC= BC.sin B= BC.cos C$<br\/>C\u00e2u C \u0111\u00fang<br\/>C\u00e2u D sai, v\u00ec nh\u1ea7m c\u00f4ng th\u1ee9c $AC= AB.tg B= AB.cotg C$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span>","column":2}]}],"id_ques":1343},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Gi\u1ea3i tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, bi\u1ebft $AB= 21$; $AC=18$.","select":["A. $\\widehat{B}\\approx 41^{o};$$\\,\\widehat{C}\\approx 49^{o}$; $\\, BC\\approx 27,437$","B. $\\widehat{B}\\approx 41^{o};$$\\,\\widehat{C}\\approx 49^{o}$; $\\, BC\\approx 25,628$ ","C. $\\widehat{B}\\approx 41^{o};$$\\,\\widehat{C} \\approx 38^{o}$; $\\, BC\\approx 26,284$","D. $\\widehat{B}\\approx 41^{o};$$\\,\\widehat{C} \\approx 49^{o}$; $\\, BC\\approx 28,182$"],"explain":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D8.png' \/><\/center><br\/><span class='basic_left'>X\u00e9t $\\Delta ABC$ c\u00f3: $\\widehat{A}=90^{o}$<br\/>\u00c1p d\u1ee5ng t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c trong tam gi\u00e1c vu\u00f4ng<br\/> $tg B=\\dfrac{AC}{AB}=\\dfrac{18}{21}$$\\Rightarrow \\widehat{B}\\approx 41^{o}$ <br\/> $\\Rightarrow \\widehat{C}=90^{o}-\\widehat{B}\\approx 90^{o} - 41^{o}= 49^{o}$ ($\\widehat{B}$ v\u00e0 $\\widehat{C}$ ph\u1ee5 nhau) <br\/>X\u00e9t tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$ <br\/> \u00c1p d\u1ee5ng t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c trong tam gi\u00e1c vu\u00f4ng, ta c\u00f3: <br\/> $BC=\\dfrac{AC}{sin\\, B}\\,$$=\\dfrac{18}{sin\\,41^{o}}\\approx 27,437$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":1344},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["112,97"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D5.png' \/><\/center><br\/>Tr\u00ean b\u1edd kia c\u1ee7a d\u00f2ng s\u00f4ng l\u1ea5y \u0111i\u1ec3m $B$, b\u1edd b\u00ean n\u00e0y l\u1ea5y \u0111i\u1ec3m $A$ \u0111\u1ed1i di\u1ec7n v\u1edbi \u0111i\u1ec3m $B$. \u0110\u1ec3 \u0111o gi\u00e1n ti\u1ebfp \u0111\u1ed9 r\u1ed9ng c\u1ee7a d\u00f2ng s\u00f4ng (kho\u1ea3ng c\u00e1ch $AB$), ng\u01b0\u1eddi ta l\u1ea5y \u0111i\u1ec3m $C$ b\u00ean n\u00e0y d\u00f2ng s\u00f4ng v\u00e0 c\u00e1ch $A$ m\u1ed9t kho\u1ea3ng $AC=79 m$, \u0111\u1eb7t gi\u00e1c k\u1ebf t\u1ea1i $C$ \u0111o \u0111\u01b0\u1ee3c g\u00f3c $\\widehat{ACB}=55^{o}$. T\u00ednh chi\u1ec1u r\u1ed9ng c\u1ee7a con s\u00f4ng. <br\/>(Cho bi\u1ebft $sin 55^o=0,82;\\, cos 55^o=0,57;\\, tg 55^o=1,43;\\, cotg 55^o=0,7$)<br\/><b> \u0110\u00e1p s\u1ed1:<\/b> _input_$(m)$<\/span> ","explain":"<span class='basic_left'><br\/>X\u00e9t $\\Delta ABC$ c\u00f3: $\\widehat{A}=90^{o}$. <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng.<br\/>Ta c\u00f3:<br\/>$AB=AC.tg C=79.tg 55^o=112,97\\, (m)$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $112,97$<\/span><\/span>"}]}],"id_ques":1345},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["DE","ED"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Cho h\u00ecnh v\u1ebd:<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D2.png' \/><br\/><\/center>$\\,\\,\\,$_input_$=DF.tg F$","hint":"Trong tam gi\u00e1c vu\u00f4ng, m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng c\u1ea1nh g\u00f3c vu\u00f4ng kia nh\u00e2n v\u1edbi tg g\u00f3c \u0111\u1ed1i ho\u1eb7c nh\u00e2n v\u1edbi cotg g\u00f3c k\u1ec1","explain":"Tam gi\u00e1c $DEF$ vu\u00f4ng t\u1ea1i $D$ n\u00ean ta c\u00f3: $DE= DF.tg F$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $DE$<\/span>"}]}],"id_ques":1346},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","f","t","t"]],"list":[{"point":5,"image":"","col_name":["<img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D2b.png' \/><br\/>Trong tam gi\u00e1c vu\u00f4ng $A$, c\u1ea1nh huy\u1ec1n $BC=a$ v\u00e0 c\u00e1c c\u1ea1nh g\u00f3c vu\u00f4ng $AC=b,\\,AB= c$. Khi \u0111\u00f3","\u0110\u00fang","Sai"],"arr_ques":["$b=a.sin B$","$b=a.tg \\, B$","$c=b.tg \\,C$","$c=a.cos\\, B$"],"explain":["\u0110\u00fang v\u00ec: $sin B =\\dfrac {AC}{BC}=\\dfrac {b}{a}\\Rightarrow b=a sin {B}$","<br\/>Sai v\u00ec, $tg \\, B=\\dfrac {AC}{AB}=\\dfrac {b}{c}\\Rightarrow b=c. tg\\, B$","<br\/>\u0110\u00fang v\u00ec, $tg\\, C=\\dfrac {AB}{AC}=\\dfrac {c}{b}\\Rightarrow c=b.tg\\,C$","<br\/>\u0110\u00fang v\u00ec, $cos \\,B=\\dfrac {AB}{BC}=\\dfrac {c}{a}\\Rightarrow c=a.cos \\, B$"]}]}],"id_ques":1347},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ \u0111\u1ec1u, c\u1ea1nh $AC= 6cm.$ L\u1ea5y \u0111i\u1ec3m $D$ thu\u1ed9c tia \u0111\u1ed1i c\u1ee7a tia $BC$ sao cho g\u00f3c $\\widehat {ADB}=35^{o}$. K\u1ebb $AH$ vu\u00f4ng g\u00f3c v\u1edbi $BC$ t\u1ea1i $H$. <br\/><b> C\u00e2u 1:<\/b> \u0110\u1ed9 d\u00e0i c\u1ea1nh $AD$ b\u1eb1ng: <\/span><br\/><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D25.png' \/>","select":["A. $6,34 cm$","B. $5,23 cm$","C. $9,06 cm$","D. $4,25 cm$"],"hint":"T\u00ednh c\u1ea1nh $AH$","explain":" <span class='basic_left'>Ta c\u00f3: $\\Delta ABC$ \u0111\u1ec1u (gi\u1ea3 thi\u1ebft) $\\Rightarrow \\widehat{A}=\\widehat{B}=\\widehat{C}=60^{o}$ (\u0111\u1ecbnh ngh\u0129a)<br\/>X\u00e9t $\\Delta ABH$ c\u00f3: $ \\widehat {H}=90^{o}$ <br\/> $\\Rightarrow AH= AB.sin\\,60^{o}$ (h\u1ec7 th\u1ee9c v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AH =6.\\dfrac{\\sqrt{3}}{2}=3\\sqrt{3}(\\,cm) $<br\/>X\u00e9t $\\Delta ADH$ c\u00f3: $ \\widehat{H}=90^{o}$ <br\/> $AH=AD.sin\\,\\widehat{ADB}$ (h\u1ec7 th\u1ee9c v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AD=\\dfrac{AH}{sin\\,35^{o}}\\,$$=\\dfrac{3\\sqrt{3}}{sin\\,35^{o}}\\approx 9,06 (cm)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":4}]}],"id_ques":1348},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["4,42"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ \u0111\u1ec1u, c\u1ea1nh $AC= 6cm.$ L\u1ea5y \u0111i\u1ec3m $D$ thu\u1ed9c tia \u0111\u1ed1i c\u1ee7a tia $BC$ sao cho g\u00f3c $\\widehat {ADB}=35^{o}$. K\u1ebb $AH$ vu\u00f4ng g\u00f3c v\u1edbi $BC$ t\u1ea1i $H$. <br\/><b> C\u00e2u 2:<\/b> \u0110\u1ed9 d\u00e0i c\u1ea1nh $DB$ l\u00e0_input_ $(cm)$<br\/>(K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai) <\/span><br\/><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D25.png' \/>","explain":" <span class='basic_left'>Ta c\u00f3 tam gi\u00e1c $ABC$ \u0111\u1ec1u (gi\u1ea3 thi\u1ebft). Suy ra: $AB=AC=BC=6cm$ <br\/> L\u1ea1i c\u00f3: $AH\\bot BC$ t\u1ea1i $H$ <br\/> $\\Rightarrow BH=HC=\\dfrac{BC}{2}=3\\, (cm)$ (t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung cao trong tam gi\u00e1c \u0111\u1ec1u) <br\/>Theo c\u00e2u 1, ta c\u00f3: $AH=3\\sqrt{3}\\,(cm)$ <br\/> X\u00e9t $\\Delta ADH$ c\u00f3: $ \\widehat {H}=90^{o}$<br\/>$\\Rightarrow DH= AH.cotg\\,\\widehat{ADB}$ (h\u1ec7 th\u1ee9c v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow DH=3\\sqrt{3}.cotg\\,35^{o}\\approx 7,42 \\,(cm)$<br\/>Suy ra: $DB=DH -BH\\approx 7,42-3=4,42 \\,(cm)$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $4,42$<\/span><\/span>"}]}],"id_ques":1349},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, $AC= 5 cm$, $\\widehat{C}=32^{o}$. \u0110\u1ed9 d\u00e0i c\u1ea1nh $AB$ x\u1ea5p x\u1ec9 b\u1eb1ng: ","select":["A. $3,6 cm$","B. $3,5 cm$","C. $3,1 cm$","D. $2,9 cm$"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D16.png' \/><\/center><br\/> <span class='basic_left'>X\u00e9t $\\Delta ABC$ vu\u00f4ng t\u1ea1i $A$.<br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng, ta c\u00f3:<br\/> $AB= AC.tg \\,C= 5.tg 32^{o}\\approx 3,1 \\,(cm)$<br\/>V\u1eady \u0111\u1ed9 d\u00e0i $AB$ x\u1ea5p x\u1ec9 $3,1\\, cm$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span>","column":4}]}],"id_ques":1350},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t \u0111\u1ec3 \u0111i\u1ec1n v\u00e0o ph\u1ea7n c\u00f2n thi\u1ebfu","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng . . . nh\u00e2n v\u1edbi tang g\u00f3c \u0111\u1ed1i ho\u1eb7c . . . g\u00f3c k\u1ec1 ","select":["A. c\u1ea1nh g\u00f3c vu\u00f4ng c\u00f2n l\u1ea1i, c\u00f4sin","B. c\u1ea1nh huy\u1ec1n, c\u00f4tang ","C. c\u1ea1nh huy\u1ec1n, c\u00f4sin","D. c\u1ea1nh g\u00f3c vu\u00f4ng c\u00f2n l\u1ea1i, c\u00f4tang"],"explain":" Trong m\u1ed9t tam gi\u00e1c vu\u00f4ng, m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng <b> c\u1ea1nh g\u00f3c vu\u00f4ng c\u00f2n l\u1ea1i <\/b> nh\u00e2n v\u1edbi tang g\u00f3c \u0111\u1ed1i ho\u1eb7c <b> c\u00f4tang <\/b> g\u00f3c k\u1ec1<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span>","column":2}]}],"id_ques":1351},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["BC","CB"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Cho h\u00ecnh v\u1ebd:<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D1.png' \/><\/center><br\/>$AC=$_input_$cos \\,C$","hint":"Trong tam gi\u00e1c vu\u00f4ng, m\u1ed7i c\u1ea1nh g\u00f3c vu\u00f4ng b\u1eb1ng c\u1ea1nh huy\u1ec1n nh\u00e2n v\u1edbi sin g\u00f3c \u0111\u1ed1i ho\u1eb7c nh\u00e2n v\u1edbi c\u00f4sin g\u00f3c k\u1ec1 ","explain":"<span class='basic_left'>Tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$ ta c\u00f3:<br\/>$AC= BC.cos C$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $BC$<\/span><\/span>"}]}],"id_ques":1352},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4,5"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>M\u1ed9t chi\u1ebfc m\u00e1y bay bay l\u00ean v\u1edbi v\u1eadn t\u1ed1c $450 km\/h$. \u0110\u01b0\u1eddng bay l\u00ean t\u1ea1o v\u1edbi ph\u01b0\u01a1ng n\u1eb1m ngang m\u1ed9t g\u00f3c $30 ^{o}$ (bi\u1ec3u di\u1ec5n nh\u01b0 h\u00ecnh 1). H\u1ecfi sau $1,2$ ph\u00fat m\u00e1y bay l\u00ean cao \u0111\u01b0\u1ee3c bao nhi\u00eau kil\u00f4m\u00e9t theo ph\u01b0\u01a1ng th\u1eb3ng \u0111\u1ee9ng?<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D3.png' \/><\/center><br\/><b> \u0110\u00e1p s\u1ed1: <\/b> _input_$(km)$<br\/> (K\u1ebft qu\u1ea3 vi\u1ebft d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n)<\/span> ","hint":"$BH$ ch\u00ednh l\u00e0 \u0111\u1ed9 cao m\u00e1y bay \u0111\u1ea1t \u0111\u01b0\u1ee3c sau $1,2$ ph\u00fat \u0111\u00f3.","explain":"<span class='basic_left'>Gi\u1ea3 s\u1eed trong h\u00ecnh 1, $AB$ l\u00e0 \u0111o\u1ea1n \u0111\u01b0\u1eddng m\u00e1y bay l\u00ean trong $1,2$ ph\u00fat th\u00ec $BH$ ch\u00ednh l\u00e0 \u0111\u1ed9 cao m\u00e1y bay \u0111\u1ea1t \u0111\u01b0\u1ee3c sau $1,2$ ph\u00fat \u0111\u00f3.<br\/>Ta c\u00f3: $1,2$ ph\u00fat $=\\dfrac{1}{50}$ gi\u1edd n\u00ean $\\,AB=\\dfrac{450}{50}=9\\,(km)$<br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng $ABC,$ ta c\u00f3: <br\/> $BH=AB.sin\\,30^{o}=9.\\dfrac{1}{2}=4,5 \\,(km)$ <br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $4,5$ <\/span><\/span>"}]}],"id_ques":1353},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Gi\u1ea3i tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$, bi\u1ebft $\\widehat{B}=36^{o}$ v\u00e0 $BC= 7$.","select":["A. $\\widehat{C}=54^{o};$$\\,AB\\approx 5,684$; $\\, AC\\approx 4,772$","B. $\\widehat{C}=54^{o};$$\\,AB\\approx 5,663$; $\\, AC\\approx 4,114$ ","C. $\\widehat{C}=54^{o};$$\\,AB\\approx 4,114$; $\\, AC\\approx 5,663$","D. $\\widehat{C}=54^{o};$$\\,AB\\approx 6,241$; $\\, AC\\approx 5,214$"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D7.png' \/><\/center><br\/><span class='basic_left'>X\u00e9t $\\Delta ABC$ c\u00f3: $\\widehat{A}=90^{o}$ <br\/> $\\Rightarrow\\widehat{C}=90^{o}-\\widehat{B}=90^{o}-36^{o}=54^{o}$ ($\\widehat{B}$ v\u00e0 $\\widehat{C}$ ph\u1ee5 nhau) <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng $ABC,$ ta c\u00f3:<br\/> $AB=BC.sin \\widehat{C} =7.sin 54^{o}\\approx 5,663$<br\/>$AC=BC.sin \\,B=7.sin 36^{o}\\approx 4,114$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span><\/span>","column":2}]}],"id_ques":1354},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Cho tam gi\u00e1c $DEF$ vu\u00f4ng t\u1ea1i $E$.","select":["A. $EF=DF.sin D$","B. $EF=DF.cos D$","C. $DE=DF.tg F$","D. $DE=DF.cotg D$"],"explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D12.png' \/><\/center><br\/> C\u00e2u A \u0111\u00fang<br\/>C\u00e2u B sai, v\u00ec nh\u1ea7m c\u00f4ng th\u1ee9c $EF=DF.sin D=DF.cos F$<br\/>C\u00e2u C sai, v\u00ec nh\u1ea7m c\u00f4ng th\u1ee9c $DE=EF.tg F=EF.cotg D$<br\/>C\u00e2u D sai, v\u00ec nh\u1ea7m c\u00f4ng th\u1ee9c $DE=EF.tg F=EF.cotg D$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span>","column":2}]}],"id_ques":1355},{"time":24,"part":[{"title":"Kh\u1eb3ng \u0111\u1ecbnh sau \u0110\u00fang hay Sai","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'>Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A$ c\u00f3 $AB=3AC$. Tr\u00ean $AB$ l\u1ea5y c\u00e1c \u0111i\u1ec3m $D$ v\u00e0 $E$ sao cho $AD=DE=EB$.<br\/> Khi \u0111\u00f3:$\\,tg \\,\\widehat{AEC}+\\,tg\\,\\widehat{ABC}=\\dfrac{5}{6}$<\/span>","select":["A. \u0110\u00fang","B. Sai"],"hint":"X\u00e9t tam gi\u00e1c $ACE$, t\u00ecnh $tg \\,E$ v\u00e0 x\u00e9t tam gi\u00e1c $ABC$, t\u00ednh $tg\\, B$. T\u1eeb \u0111\u00f3 xem kh\u1eb3ng \u0111\u1ecbnh c\u00f3 \u0111\u00fang kh\u00f4ng?","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D23.png' \/><\/center><br\/><span class='basic_left'>X\u00e9t $\\Delta ACE$ c\u00f3: $ \\widehat{A}=90^{o}$ (gi\u1ea3 thi\u1ebft)<br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng v\u00e0o tam gi\u00e1c vu\u00f4ng $ACE$ ta c\u00f3:<br\/>$ tg \\,\\widehat{AEC}=\\dfrac{AC}{AE}=\\dfrac{1}{2}$<br\/>X\u00e9t $ \\Delta ABC$ c\u00f3: $\\widehat{A}=90^{o}$ (gi\u1ea3 thi\u1ebft)<br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng v\u00e0o tam gi\u00e1c vu\u00f4ng $ABC$ ta c\u00f3:<br\/>$tg \\, \\widehat{ABC}=\\dfrac{AC}{AB}=\\dfrac{1}{3}$<br\/> $\\Rightarrow tg \\,\\widehat{AEC}+\\,tg\\,\\widehat{ABC}=\\dfrac{1}{2}+\\dfrac{1}{3}=\\dfrac{5}{6}$<br\/>V\u1eady kh\u1eb3ng \u0111\u1ecbnh tr\u00ean l\u00e0 \u0110\u00fang<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":1356},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["3"],["2"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","input_hint":[""],"ques":"<span class='basic_left'>Trong tam gi\u00e1c $ABC$ c\u00f3 $AB=6\\,cm;$ $\\,\\widehat{ABC}={{30}^{o}};\\widehat{ACB}={{45}^{o}}$, $H$ l\u00e0 ch\u00e2n \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c k\u1ebb t\u1eeb $A$ \u0111\u1ebfn $BC$. \u0110\u1ed9 d\u00e0i c\u1ea1nh $AC$ l\u00e0 $\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}\\sqrt{\\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}}\\,(cm)$<\/span> ","hint":"X\u00e9t tam gi\u00e1c $ABH$, t\u00ednh $AH$","explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D20.png' \/><\/center><br\/>X\u00e9t $\\Delta AHB$ vu\u00f4ng t\u1ea1i $H$ ta c\u00f3: <br\/> $AH=AB.sin \\widehat{ABC}$ (h\u1ec7 th\u1ee9c v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AH =6.sin {{30}^{o}}=3\\left( cm \\right)$ <br\/>X\u00e9t $\\Delta ACH$ vu\u00f4ng t\u1ea1i $H$ ta c\u00f3: <br\/> $AH=AC.sin \\widehat{ACB}$ (h\u1ec7 th\u1ee9c v\u1ec1 c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng) <br\/> $\\Rightarrow AC=\\dfrac{AH}{sin \\widehat{ACB}}\\,$$=\\dfrac{3}{\\dfrac {\\sqrt 2}{2}}=3\\sqrt {2}\\left( cm \\right)$ <br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $3\\sqrt {2}$<\/span><\/span>"}]}],"id_ques":1357},{"time":24,"part":[{"time":3,"title":"H\u00e3y n\u1ed7i m\u1ed7i \u00f4 \u1edf c\u1ed9t tr\u00e1i v\u1edbi m\u1ed9t \u00f4 \u1edf c\u1ed9t ph\u1ea3i \u0111\u1ec3 \u0111\u01b0\u1ee3c kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang","title_trans":"","audio":"","temp":"matching","correct":[["2","1","3"]],"list":[{"point":5,"image":"","left":["Tam gi\u00e1c $ABC$ vu\u00f4ng c\u00e2n t\u1ea1i $A$ th\u00ec ","Tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $C$ th\u00ec","Tam gi\u00e1c $ABC $ \u0111\u1ec1u th\u00ec "],"right":["$cos\\,B=\\dfrac{BC}{AB}$","$tg \\,B= 1$","$sin\\,A=\\dfrac{\\sqrt{3}}{2}$"],"top":100,"explain":"<span class='basic_left'>Tam gi\u00e1c $ABC$ vu\u00f4ng c\u00e2n t\u1ea1i $A$. Suy ra, $\\widehat {B}=\\widehat {C}=45^o$ <br\/> Khi \u0111\u00f3, $tg\\,B=tg\\, {45^o}= 1$ <br\/> Tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $C$ th\u00ec $cos\\,B=\\dfrac{BC}{AB}$ <br\/> Tam gi\u00e1c $ABC$ \u0111\u1ec1u th\u00ec $sin\\,A=sin\\,{60^o}=\\dfrac{\\sqrt{3}}{2}$ <\/span>"}]}],"id_ques":1358},{"time":24,"part":[{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $4\\sqrt{3}$","B. $3\\sqrt{3}$","C. $2\\sqrt{3}$"],"ques":"Cho tam gi\u00e1c $ABC$ c\u00f3 $BC= 8cm$; $\\widehat{B}=60^{o};\\,\\widehat{C}=40^{o}$. K\u1ebb $CH$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $H$<br\/><b> C\u00e2u 1 : <\/b> \u0110\u1ed9 d\u00e0i c\u1ea1nh $CH$ l\u00e0 ? $(cm)$","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D26.png' \/><\/center><br\/>X\u00e9t $\\Delta BHC$ c\u00f3: $ \\widehat{H}=90^{o}$ ($CH$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $H$)<br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng $BHC$ ta c\u00f3:<br\/>$ CH=BC.sin \\,\\widehat{ABC}=8.sin\\,60^{o}=4\\sqrt{3} \\,(cm)$<\/span>"}]}],"id_ques":1359},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u1ebft qu\u1ea3 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["7,04"]]],"list":[{"point":5,"width":40,"content":"","type_input":"","type_check":"","ques":"Cho tam gi\u00e1c $ABC$ c\u00f3 $BC= 8\\,cm$; $\\widehat{B}=60^{o};\\,\\widehat{C}=40^{o}$. K\u1ebb $CH$ vu\u00f4ng g\u00f3c v\u1edbi $AB$ t\u1ea1i $H$<br\/><b> C\u00e2u 2: <\/b> \u0110\u1ed9 d\u00e0i c\u1ea1nh $AC\\approx $_input_ $(cm)$<br\/>(K\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n \u0111\u1ebfn s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai)","hint":"T\u00ednh g\u00f3c $A$, r\u1ed3i \u00e1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng $AHC$ \u0111\u1ec3 t\u00ednh $AC$","explain":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai3/lv1/img\/H913_D26.png' \/><\/center><span class='basic_left'>Theo c\u00e2u 1, ta c\u00f3: $CH=4\\sqrt{3}\\,(cm)$ <br\/> X\u00e9t $\\Delta ABC$ c\u00f3: $ \\widehat{A}+\\widehat{B}+\\widehat{C}=180^{o}\\\\ \\Rightarrow\\widehat{A}=180^{o}-60^{o} -40^{o}\\\\ \\Rightarrow \\widehat{A}=80^{o} $ <br\/> X\u00e9t $\\Delta AHC$ c\u00f3: $\\widehat{H}=90^{o}$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng $AHC$ ta c\u00f3:<br\/>$CH=AC.sin\\,\\widehat{A} \\Rightarrow AC = \\dfrac{CH}{sin\\,\\widehat{A}} \\Rightarrow AC= \\dfrac{4\\sqrt{3}}{sin\\,80^{o}}\\approx 7,04 (cm)$<br\/><span class='basic_pink'>V\u1eady c\u1ea7n \u0111i\u1ec1n v\u00e0o ch\u1ed7 tr\u1ed1ng l\u00e0 $7,04$<\/span><\/span>"}]}],"id_ques":1360}],"lesson":{"save":0,"level":1}}