Txhawm rau xam thaj tsam ntawm daim duab peb sab, koj yuav tsum paub nws qhov siab. Yog tias cov ntaub ntawv no tsis paub nyob hauv qhov teeb meem, koj tuaj yeem suav nws yooj yim raws li cov ntaub ntawv paub. Kab lus no yuav coj koj mus nrhiav qhov siab ntawm daim duab peb sab siv peb txoj hauv kev sib txawv, raws li paub cov ntaub ntawv.
Kauj ruam
Txoj Kev 1 ntawm 3: Siv Lub Hauv Paus thiab Cheeb Tsam txhawm rau Nrhiav Qhov Siab
Kauj Ruam 1. Rov qab cov mis rau thaj tsam ntawm daim duab peb sab
Cov mis rau thaj tsam ntawm daim duab peb sab yog L = 1/2 ib.
- L = cheeb tsam ntawm daim duab peb sab
- a = ntev ntawm lub hauv paus ntawm daim duab peb sab
- t = qhov siab ntawm daim duab peb sab los ntawm lub hauv paus
Kauj Ruam 2. Saib daim duab peb sab hauv qhov teeb meem thiab txiav txim siab qhov twg tuaj yeem hloov pauv
Hauv txoj hauv kev ntawm no, thaj tsam ntawm daim duab peb sab tau paub, yog li sau tus nqi ntawd ua qhov sib txawv L. Koj kuj yuav tsum paub qhov ntev ntawm ib sab, sau tus nqi ntawd ua qhov sib txawv a. Yog tias koj tsis paub thaj chaw thiab hauv paus ntawm daim duab peb sab, koj yuav tsum siv lwm txoj hauv kev los xam.
- Tsis hais txog kev piav qhia ntawm cov duab ntawm daim duab peb sab, ib sab tuaj yeem yog lub hauv paus. Txhawm rau nkag siab qhov no, xav txog qhov tig ib daim duab peb sab kom paub tias sab ntawm lub hauv paus.
- Piv txwv, yog tias koj paub thaj tsam ntawm daim duab peb sab yog 20, thiab qhov ntev ntawm ib sab yog 4, sau: L = 20 hli thiab ib = 4.
Kauj Ruam 3. Plug qhov paub qhov tseem ceeb rau hauv cov mis L = 1/2at thiab suav
Ua ntej, muab lub hauv paus (a) los ntawm 1/2, tom qab ntawd faib thaj tsam (L) los ntawm qhov tshwm sim. Tus nqi tau txais yog qhov siab ntawm koj daim duab peb sab!
- Hauv qhov piv txwv ntawm no: 20 = 1/2 (4) t
- 20 = 2 hli
- 10 = ttw
Txoj Kev 2 ntawm 3: Nrhiav Qhov Siab ntawm Ib Daim Duab Peb Hlis
Kauj Ruam 1. Nco qab cov khoom ntawm daim duab peb sab
Ib daim duab peb sab sib npaug muaj 3 sab sib npaug thiab peb lub kaum sib npaug sib npaug, txhua 60 degrees. Yog tias daim duab peb sab sib npaug tau muab faib ua ob qho sib npaug, koj yuav tau txais ob daim duab peb sab sib xws.
Hauv qhov piv txwv ntawm no, peb yuav siv daim duab peb sab sib npaug nrog txhua sab ntev ntawm 8
Kauj Ruam 2. Rov nco txog Pythagorean Theorem
Pythagorean theorem hais tias rau txhua txoj cai peb tog uas muaj sab ntev a thiab b, nrog rau hypotenuse c thov: a2 + b2 = c2. Peb tuaj yeem siv cov qauv no los nrhiav qhov siab ntawm daim duab peb sab sib npaug!
Kauj Ruam 3. Muab faib daim duab peb sab sib npaug ua ob ntu sib npaug, thiab kos ob sab ua qhov hloov pauv a, b, thiab c.
Ntev ntawm hypotenuse c yuav sib npaug rau qhov ntev ntawm ib sab ntawm daim duab peb sab equilateral. Sab a yuav sib npaug li 1/2 qhov ntev ntawm sab ua ntej, thiab sab b yog qhov siab ntawm daim duab peb sab los nrhiav.
Siv qhov piv txwv ntawm daim duab peb sab sib npaug nrog sab ntev = 8 c = 8 hli thiab ib = 4.
Kauj Ruam 4. Plug tus nqi no rau hauv Pythagorean Theorem thiab nrhiav tus nqi b2.
Thawj lub xwmfab c thiab a los ntawm kev sib npaug txhua tus lej los ntawm tus lej qub. Tom qab ntawd, rho tawm a2 los ntawm c2.
- 42 + b2 = 82
- 16 + ib2 = 64
- b2 = 48
Kauj Ruam 5. Nrhiav lub hauv paus cag ntawm b2 kom paub qhov siab ntawm koj daim duab peb sab!
Siv cov xwm txheej hauv paus hauv koj lub laij lej kom pom Sqrt (2). Qhov txiaj ntsig ntawm kev suav yog qhov siab ntawm koj daim duab peb sab sib npaug!
b = Sqrt (48) = 6, 93
Txoj Kev 3 ntawm 3: Nrhiav Qhov Siab nrog Lub Kaum thiab Sab Ntev
Kauj Ruam 1. Txheeb xyuas qhov paub sib txawv
Koj tuaj yeem pom qhov siab ntawm daim duab peb sab yog tias koj paub lub kaum sab xis thiab qhov ntev ntawm sab, yog tias lub kaum sab xis nyob nruab nrab ntawm lub hauv paus thiab paub sab, lossis txhua sab ntawm daim duab peb sab. Peb hu ob sab ntawm daim duab peb sab a, b, thiab c, thaum cov ces kaum hu ua A, B, thiab C.
- Yog tias koj paub qhov ntev ntawm peb sab, koj tuaj yeem siv Heron cov mis, thiab cov mis rau thaj tsam ntawm daim duab peb sab.
- Yog tias koj paub qhov ntev ntawm ob sab ntawm daim duab peb sab thiab lub kaum ntse ntse, koj tuaj yeem siv cov qauv rau thaj tsam ntawm daim duab peb sab raws li cov ntaub ntawv ntawd. L = 1/2 AB (sin C).
Kauj Ruam 2. Siv Heron tus qauv yog tias koj paub qhov ntev ntawm peb lub kaum sab xis ntawm daim duab peb sab
Heron tus qauv muaj ob ntu. Ua ntej, koj yuav tsum nrhiav qhov sib txawv s, uas yog sib npaug ib nrab ntawm qhov puag ncig ntawm daim duab peb sab. Koj tuaj yeem suav nws siv cov mis: s = (a+b+c)/2.
- Yog li rau daim duab peb sab nrog a = 4, b = 3, thiab c = 5, s = (4+3+5)/2. Yog li s = (12)/2, s = 6.
- Tom qab ntawd, koj tuaj yeem txuas ntxiv suav nrog siv ntu thib ob ntawm Heron tus lej, Cheeb Tsam = sqr (s (s-a) (s-b) (s-c)). Hloov thaj tsam tus nqi hauv cov mis nrog nws sib npaug hauv daim duab peb sab thaj tsam: 1/2bt (lossis 1/2at lossis 1/2ct).
- Ua cov lej los nrhiav tus nqi ntawm t. Hauv qhov piv txwv ntawm no, xam yog 1/2 (3) t = sqr (6 (6-4) (6-3) (6-5)). Yog li 3/2t = sqr (6 (2) (3) (1)), uas muab 3/2t = sqr (36). Siv lub laij lej los xam cov hauv paus plaub fab, yog li koj tau txais 3/2t = 6. Yog li, qhov siab ntawm daim duab peb sab ntawm no yog 4, nrog b ua lub hauv paus.
Kauj Ruam 3. Siv cov qauv rau thaj tsam ntawm daim duab peb sab nrog ob sab thiab ib lub kaum, yog tias koj paub ib sab thiab ib lub kaum sab xis ntawm daim duab peb sab
Hloov thaj tsam ntawm daim duab peb sab nrog cov qauv sib npaug: 1/2at. Txoj kev ntawd, koj yuav tau txais cov mis zoo li cov hauv qab no: 1/2bt = 1/2ab (sin C). Cov mis no tuaj yeem ua kom yooj yim rau t = a (sin C), los ntawm kev tshem tawm sab nraud ntawm qhov sib txawv.
