{"segment":[{"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["0"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","type_check":"","ques":"T\u00ednh $tg\\, 79^o - cotg\\, 11^o=$_input_","hint":"Hai g\u00f3c nh\u1ecdn ph\u1ee5 nhau th\u00ec sin g\u00f3c n\u00e0y b\u1eb1ng c\u00f4sin g\u00f3c kia v\u00e0 tang g\u00f3c n\u00e0y b\u1eb1ng c\u00f4tang g\u00f3c kia","explain":"Ta c\u00f3:<br\/>$tg\\, 79^o - cotg\\, 11^o\\\\ =tg\\, 79^o -tg\\, (90^o-11^o)\\\\ = tg\\, 79^o- tg\\, 79^o \\\\ = 0$<br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $0.$<\/span>"}],"id_ques":1401},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["AH","HA"],["AB","BA"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho h\u00ecnh v\u1ebd <br\/><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_5.png' \/> <br\/> _input_$=AB.sin\\, B $;$ AC=$_input_$.tg\\, B$<\/span>","explain":"<span class='basic_left'> X\u00e9t $\\Delta ABH$ vu\u00f4ng t\u1ea1i $H$ <br\/> $sin\\, B = \\dfrac{AH}{AB}$ (t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn) <br\/> $\\Rightarrow AH=AB.sin\\, B$ <br\/> X\u00e9t $ \\Delta ABC$ vu\u00f4ng t\u1ea1i $A$ <br\/> $tg\\, B = \\dfrac{AC}{AB}$ (t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn) <br\/>$\\Rightarrow AC=AB.tg\\, B$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 $AH, AB$<\/span>"}],"id_ques":1402},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["20"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho h\u00ecnh v\u1ebd<br\/><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_6a.png' \/> <br\/>Gi\u00e1 tr\u1ecb c\u1ee7a $x$ l\u00e0_input_","hint":"\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $\\dfrac{1}{h^2}=\\dfrac{1}{a^2}+\\dfrac{1}{b^2}$ ","explain":"<span class='basic_left'> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $\\dfrac{1}{h^2}=\\dfrac{1}{a^2}+\\dfrac{1}{b^2}$ ta c\u00f3:<br\/>$\\dfrac{1}{12^2}=\\dfrac{1}{15^2}+\\dfrac{1}{x^2}\\\\ \\Leftrightarrow\\dfrac{1}{x^2}=\\dfrac{1}{12^2}-\\dfrac{1}{15^2}\\\\ \\Leftrightarrow \\dfrac{1}{x^2}=\\dfrac{1}{400}\\\\ \\Rightarrow x= 20$<br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $20.$ <\/span> "}],"id_ques":1403},{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A,$ \u0111\u01b0\u1eddng cao $AH,$ bi\u1ebft $AH= 2 cm, HB= 2\\sqrt{3} cm.$ Khi \u0111\u00f3, s\u1ed1 \u0111o g\u00f3c $C$ l\u00e0: ","select":["A. $30^o$ ","B. $45^o$","C. $60^o$","D. $90^o$"],"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_5.png' \/><\/center><br\/> X\u00e9t $\\Delta ABC$ vu\u00f4ng t\u1ea1i $A$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $h^2=b'.c'$ ta c\u00f3: <br\/> $AH^2=HB.HC $ <br\/> $\\Rightarrow HC=\\dfrac{AH^2}{HB}$$=\\dfrac{4}{2\\sqrt{3}}=\\dfrac{2}{\\sqrt{3}}$ <br\/> X\u00e9t $\\Delta AHC$ vu\u00f4ng t\u1ea1i $H$ <br\/>$tg\\, C=\\dfrac{AH}{HC}$$=\\dfrac{2}{\\dfrac{2}{\\sqrt{3}}}=\\sqrt{3}\\Rightarrow \\widehat{C} =60^o$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 C<\/span><\/span>","column":4}],"id_ques":1404},{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"T\u00ednh $cotg\\, 21^o.cotg\\, 30^o .cotg\\,69^o$","select":["A. $1$","B. $\\sqrt{3}$","C. $\\dfrac{1}{2}$","D. $\\dfrac{\\sqrt{3}}{3}$"],"hint":"Hai g\u00f3c ph\u1ee5 nhau th\u00ec tg g\u00f3c n\u00e0y b\u1eb1ng cotg g\u00f3c kia v\u00e0 $tg\\,\\alpha.cotg\\,\\alpha=1$","explain":"<span class='basic_left'> Ta c\u00f3:<br\/>$\\,\\,\\,\\,\\,cotg\\, 21^o.cotg\\, 30^o .cotg\\, 69^o\\\\ =tg\\, (90^o - 21^o).\\sqrt{3}.cotg\\,69^o\\\\ =\\sqrt{3} .tg\\, 69^o.cotg\\,69^o\\\\ =\\sqrt{3}.1\\\\=\\sqrt{3}$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span>","column":4}],"id_ques":1405},{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"Cho tam gi\u00e1c $ABC$ vu\u00f4ng t\u1ea1i $A,$ \u0111\u01b0\u1eddng cao $AH.$ Bi\u1ebft $AB= 4 cm, AC= 7,5 cm.$ \u0110\u1ed9 d\u00e0i $HB$ l\u00e0: ","select":["A. $1\\dfrac{11}{17}\\,cm$ ","B. $1\\dfrac{15}{17}\\,cm$","C. $1\\dfrac{9}{15}\\,cm$","D. $1\\dfrac{4}{15}\\,cm$"],"explain":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_4.png' \/><\/center><br\/>$\\Delta ABC$ vu\u00f4ng t\u1ea1i $A$ <br\/> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pytago ta c\u00f3: <br\/>$BC^2=AB^2+AC^2$$\\,=4^2+7,5^2=72,25$$\\Rightarrow BC= 8,5 \\,(cm)$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c $c^2=a.c'$ ta c\u00f3: <br\/> $AB^2=BH.BC\\Rightarrow BH=\\dfrac{AB^2}{BC}$$=\\dfrac{4^2}{8,5} =1\\dfrac{15}{17}\\,(cm)$<br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 B.<\/span><\/span>","column":4}],"id_ques":1406},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["50"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","type_check":"","ques":"Tr\u00ean m\u1ed9t qu\u1ea3 \u0111\u1ed3i c\u00f3 m\u1ed9t c\u00e1i th\u00e1p cao $100m,$ t\u1eeb \u0111\u1ec9nh $B$ v\u00e0 ch\u00e2n $C$ c\u1ee7a th\u00e1p nh\u00ecn \u0111i\u1ec3m $A$ \u1edf ch\u00e2n \u0111\u1ed3i d\u01b0\u1edbi c\u00e1c g\u00f3c t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng 60$^o$ v\u00e0 30$^o$ (h\u00ecnh 1)<br\/>Chi\u1ec1u cao c\u1ee7a qu\u1ea3 \u0111\u1ed3i l\u00e0:_input_ $(m)$<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_3.png' \/><\/center>","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_3a.png' \/><\/center><br\/> C\u00e1c d\u1eef ki\u1ec7n \u0111\u00e3 cho trong \u0111\u1ec1 b\u00e0i \u0111\u01b0\u1ee3c minh h\u1ecda b\u1eb1ng h\u00ecnh v\u1ebd tr\u00ean, trong \u0111\u00f3: <br\/> $\\widehat{ABC}=90^o-60^o=30^o\\\\ \\widehat{ACB}=90^o+30^o=120^o$ <br\/> X\u00e9t $\\Delta ABC$ c\u00f3:<br\/>$\\begin{align} \\widehat{BAC}&=180^o - (\\widehat{ABC}+\\widehat{ACB})\\\\ &=180^o-(120^o+30^o)\\\\&=30^o\\\\ \\end{align}$ <br\/> Suy ra $\\Delta ABC$ c\u00e2n t\u1ea1i $A$ <br\/> $\\Rightarrow AC= CB = 100\\, (m) $<br\/>Chi\u1ec1u cao c\u1ee7a qu\u1ea3 \u0111\u1ed3i l\u00e0 \u0111o\u1ea1n $CH$.<br\/> X\u00e9t $\\Delta ACH$ vu\u00f4ng t\u1ea1i $H$ <br\/> $CH=AC.\\sin\\widehat{CAH}$$=100.\\sin 30^o=50\\, (m)$<br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $50.$<\/span>"}],"id_ques":1407},{"title":"Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"select":["A. $18\\sqrt{2}$","B. $15\\sqrt{2}$","C. $16\\sqrt{2}$"],"ques":"<span class='basic_left'>Cho h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ c\u00f3 $\\widehat{A}=45^o$; $AB=BD=18\\, cm$<br\/><b> C\u00e2u a: <\/b> \u0110\u1ed9 d\u00e0i $AD$ = ?$(cm)$<\/span>","hint":"Tam gi\u00e1c $ABD$ l\u00e0 tam gi\u00e1c g\u00ec? T\u1eeb \u0111\u00f3 t\u00ednh $AD$. ","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<br\/><\/span>B\u01b0\u1edbc 1: Ch\u1ee9ng minh tam gi\u00e1c $ABD$ vu\u00f4ng c\u00e2n t\u1ea1i $B$ <br\/>B\u01b0\u1edbc 2: \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pytago t\u00ednh c\u1ea1nh $AD$ <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <span class='basic_left'> <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_1a.png' \/><\/center><br\/>Ta c\u00f3 $AB= BD$ (gi\u1ea3 thi\u1ebft) $\\Rightarrow $ $\\Delta ABD$ c\u00e2n t\u1ea1i B<br\/>$\\widehat{BAD}=\\widehat{BDA}=45^o$ $\\Rightarrow \\widehat{ABD}=90^o$ <br\/> $\\Delta ABD$ vu\u00f4ng t\u1ea1i $B$ <br\/> \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00ed Pytago ta c\u00f3: <br\/> $AD^2=AB^2+BD^2\\\\ \\Rightarrow AD^2=18^2+18^2\\\\ \\Rightarrow AD^2=648 \\, \\\\ \\Rightarrow AD= 18\\sqrt{2} \\, (cm)$<\/span> <\/span> "}],"id_ques":1408},{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["324"]]],"list":[{"point":10,"width":40,"content":"","type_input":"","type_check":"","ques":"<span class='basic_left'>Cho h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$ c\u00f3 $\\widehat{A}=45^o$; $AB=BD=18 cm$ <br\/><b> C\u00e2u b: <\/b> Di\u1ec7n t\u00edch $ABCD$ l\u00e0_input_ $(cm^2)$<\/span>","hint":"H\u1ea1 $BH \\bot AD$ t\u1ea1i $ H $","explain":" <span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_1.png' \/><\/center> <br\/>H\u1ea1 $BH \\bot AD$ t\u1ea1i $ H $<br\/>X\u00e9t $\\Delta\\,ABH$ vu\u00f4ng t\u1ea1i $H$ <br\/> \u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c c\u1ea1nh v\u00e0 g\u00f3c trong tam gi\u00e1c vu\u00f4ng ta c\u00f3: <br\/> $BH=AB\\sin A =18\\sin45^o=18.\\dfrac{\\sqrt{2}}{2}=9\\sqrt{2}\\,(cm)$<br\/>L\u1ea1i c\u00f3: $AD=18\\sqrt{2} \\, (cm)$ (c\u00e2u a)<br\/> $S_{ABCD}=AD.BH=18\\sqrt{2}.9\\sqrt{2}=324\\,(cm^2)$<br\/><span class='basic_pink'>V\u1eady k\u1ebft qu\u1ea3 c\u1ea7n \u0111i\u1ec1n l\u00e0 $324.$<\/span><br\/><span class='basic_green'>Nh\u00e2n x\u00e9t:<\/span> Ngo\u00e0i c\u00e1ch t\u00ednh tr\u00ean, ta c\u00f3 th\u1ec3 t\u00ednh di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c b\u1eb1ng c\u00f4ng th\u1ee9c $S_{ABD}=\\dfrac{1}{2}AB.AC.\\sin A$. T\u1eeb \u0111\u00f3 t\u00ednh di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh $ABCD$.<br\/><b> C\u00e1ch 2: <\/b> $S_{ABCD}=2S_{ABD}$$\\,=2.\\dfrac{1}{2}AB.AD.\\sin A$$\\,=AB.AD.\\sin A$<br\/>$S_{ABCD}=18.18\\sqrt{2}.\\sin45^o\\\\S_{ABCD}=18.18\\sqrt{2}.\\dfrac{\\sqrt{2} }{2}\\\\S_{ABCD}=324\\,\\,(cm^2)$ <br\/><\/span>"}],"id_ques":1409},{"title":"H\u00e3y ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"Gi\u1ea3i tam gi\u00e1c vu\u00f4ng $ABC,$ bi\u1ebft $\\widehat{A}=90^o$ , $\\widehat{C}=30^o$ v\u00e0 $b= 15 cm$ ","select":["A. $\\widehat{B}=60^o$; $a \\approx 17, 32\\,cm$; $c\\approx 8,66\\,cm$ ","B. $\\widehat{B}=60^o$; $a \\approx 8,66\\,cm$; $c\\approx 17,32\\,cm$","C. $\\widehat{B}=60^o$; $a \\approx 30\\,cm$; $c\\approx 8,66\\,cm$","D. $\\widehat{B}=60^o$; $a \\approx 30\\,cm$; $c\\approx 17,32\\,cm$"],"explain":"<span class='basic_left'> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop9/toan/hinhhoc/bai5/lv3/img\/H915_2.png' \/><\/center><br\/>X\u00e9t $\\Delta ABC$ vu\u00f4ng t\u1ea1i $A$ <br\/> $ \\Rightarrow \\widehat{B}=90^o-\\widehat{C}=60^o$<br\/>\u00c1p d\u1ee5ng h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c vu\u00f4ng $ABC$, ta c\u00f3:<br\/>$c=b.tg\\, C$$=15.tg\\, 30^o $ $\\approx 8,66\\,(cm)$<br\/>$b=a.sin B $$\\Rightarrow a=\\dfrac{b}{sin\\, B}=\\dfrac{15.2}{\\sqrt{3}}$$\\approx 17,32 \\,(cm)$ <br\/><span class='basic_pink'>V\u1eady \u0111\u00e1p \u00e1n l\u00e0 A.<\/span>","column":2}],"id_ques":1410}],"id_ques":0}],"lesson":{"save":1,"level":3,"time":44}}