Nrhiav qhov puag ncig ntawm daim duab peb sab txhais tau tias nrhiav qhov nrug ib ncig ntawm daim duab peb sab. Txoj hauv kev yooj yim tshaj plaws los nrhiav qhov puag ncig ntawm daim duab peb sab yog ntxiv tag nrho txhua qhov ntev, tab sis yog tias koj tsis paub txhua sab ntev, koj yuav xav tau xam lawv ua ntej. Kab lus no yuav xub qhia koj kom pom qhov puag ncig ntawm daim duab peb sab thaum koj paub tag nrho ntev ntawm sab; Txoj kev no yog qhov yooj yim tshaj plaws thiab siv dav tshaj plaws. Tom qab ntawd, kab lus no yuav piav qhia yuav ua li cas thiaj nrhiav tau ib puag ncig ntawm daim duab peb sab xis thaum koj tsuas paub ob sab. Thaum kawg, kab lus no yuav piav qhia yuav ua li cas thiaj nrhiav tau ib puag ncig ntawm ib daim duab peb sab uas koj paub ob sab ntev thiab ntsuas qhov kaum ntawm lawv siv Txoj Cai Kev Cai.
Kauj ruam
Txoj Kev 1 ntawm 3: Nrhiav Ib puag ncig ntawm daim duab peb sab Thaum Koj Paub Txhua Yam Peb Sab
Kauj Ruam 1. Rov nco qab cov mis rau nrhiav thaj tsam
Cov mis yog: K = ib + b + c. a, b, thiab c yog qhov ntev ntawm ob sab ntawm daim duab peb sab thiab K yog qhov puag ncig ntawm daim duab peb sab.
Lub ntsiab lus ntawm cov mis no tsuas yog tias txhawm rau nrhiav qhov puag ncig ntawm daim duab peb sab, koj tsuas yog xav tau ntxiv qhov ntev ntawm txhua peb sab
Kauj Ruam 2. Saib koj daim duab peb sab thiab txiav txim siab qhov ntev ntawm nws peb sab
Hauv qhov piv txwv no, sab ntev a =
Kauj ruam 5., sab ntev b
Kauj ruam 5., thiab sab ntev c
Kauj ruam 5
Qhov piv txwv tshwj xeeb no hu ua daim duab peb sab sib npaug, vim tias tag nrho nws ob sab yog qhov ntev tib yam. Txawm li cas los xij, nco ntsoov tias cov qauv rau ib puag ncig ntawm daim duab peb sab yog tib yam rau ib daim duab peb sab
Kauj Ruam 3. Ntxiv qhov ntev ntawm peb sab kom pom qhov puag ncig ntawm daim duab peb sab
Hauv qhov piv txwv no, 5 + 5 + 5 = 15. Yog li ntawd, K = 15 hli.
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Hauv lwm qhov piv txwv, qhov twg ib = 4, b = 3 hli, thiab c = 5 hli, puag ncig ntawm daim duab peb sab yog: K = 3 + 4 + 5, los yog
Kauj ruam 12..
Kauj Ruam 4. Nco ntsoov ntxiv cov koog mus rau lo lus teb kawg
Hauv qhov piv txwv no, ob sab ntsuas hauv centimeters, yog li cov lus teb kawg yuav tsum yog hauv centimeters. Cov lus teb zaum kawg yog: K = 15 cm.
Txoj Kev 2 ntawm 3: Nrhiav Ib puag ncig ntawm Ib Daim Duab Peb Hlis los ntawm Ib Daim Duab Peb Sab Uas Paub Ob Sab
Kauj Ruam 1. Nco qab tias daim duab peb sab xis yog dab tsi
Ib daim duab peb sab yog daim duab peb sab uas muaj ib lub kaum sab xis (90 degrees). Sab ntawm daim duab peb sab tig rov qab lub kaum sab xis yog sab ntev, thiab hu ua hypotenuse. Txoj cai peb lub voos voos qhia pom ntau zaus ntawm kev xeem lej, thiab hmoov zoo muaj cov qauv yooj yim heev rau nrhiav qhov ntev ntawm ib sab tsis paub.
Kauj Ruam 2. Rov nco txog Pythagorean Theorem
Pythagorean theorem hais tias rau txhua txoj cai peb tog nrog sab ntev a thiab b, thiab hypotenuse c tuav, a2 + b2 = c2.
Kauj Ruam 3. Saib koj daim duab peb sab, thiab kos ob sab nrog "a," "b," thiab "c"
Nco ntsoov tias qhov ntev tshaj plaws ntawm daim duab peb sab hu ua hypotenuse. Sab no yuav rov qab mus rau lub kaum sab xis thiab yuav tsum tau cim raws li c. Kos rau ob sab luv li a thiab b. Nws tsis muaj teeb meem twg koj yuav kos npe rau sab twg a thiab b, qhov txiaj ntsig suav yuav zoo ib yam!
Kauj Ruam 4. Txuas qhov paub ntev ntawm sab mus rau Pythagorean Theorem
Nco ntsoov tias a2 + b2 = c2. Hloov sab ntev raws li tsab ntawv hloov pauv hauv cov mis.
- Yog tias, piv txwv li, koj paub tias sab ntev ib = 3 thiab sab b = 4 hli, tom qab ntawd, ntsaws tus nqi rau hauv cov mis raws li hauv qab no: 32 + 42 = c2.
- Yog koj paub tias sab ntev ib = 6, thiab hypotenuse c = 10 hli, tom qab ntawd koj yuav tsum nkag mus rau hauv cov mis raws li hauv qab no: 62 + b2 = 102.
Kauj Ruam 5. Daws cov kab zauv saum toj no kom pom qhov ntev ntawm sab tsis paub
Ua ntej tshaj plaws, koj yuav tsum paub lub xwmfab ntawm qhov paub sab ntev. Qhov no txhais tau tias koj yuav tsum muab sib npaug rau sab ntev los ntawm nws tus kheej tus nqi (piv txwv li 32 = 3 * 3 = 9). Yog tias koj tab tom nrhiav qhov ntev ntawm qhov hypotenuse, tsuas yog ntxiv cov xwm txheej ntawm ob sab ntawm daim duab peb sab thiab nrhiav cov hauv paus cag ntawm qhov tshwm sim. Yog tias qhov tsis paub yog lwm sab, tom qab ntawd koj yuav tsum ua qhov rho tawm yooj yim, thiab tom qab ntawd siv cov hauv paus plaub ntawm cov txiaj ntsig kom tau txais sab koj tab tom nrhiav.
- Hauv thawj qhov piv txwv, ntxiv cov xwm txheej ntawm 32 + 42 = c2 thiab tau 25 = c2. Tom qab ntawd xam lub hauv paus square ntawm 25 kom pom sab ntev c = 5 hli.
- Hauv qhov piv txwv thib ob, ntsuas qhov ntev ntawm sab hauv kab zauv 62 + b2 = 102 thiab tau 36 + ib2 = 100. Rho tawm 36 los ntawm cov xwm txheej ntawm hypotenuse, kom tau txais b2 = 64, tom qab ntawd, siv lub hauv paus cag ntawm 64 kom tau ib = 8.
Kauj Ruam 6. Ntxiv tag nrho cov sab ntev ntawm daim duab peb sab kom pom qhov puag ncig
Nco ntsoov tias puag ncig ntawm daim duab peb sab K = ib + b + c. Tam sim no koj paub txhua sab ntev ntawm daim duab peb sab a, b thiab c, koj tsuas yog xav tau ntxiv tag nrho peb qho los nrhiav qhov puag ncig.
- Hauv peb thawj qhov piv txwv, K = 3 + 4 + 5, lossis 12.
- Hauv peb qhov piv txwv thib ob, K = 6 + 8 + 10, lossis 24.
Txoj Kev 3 ntawm 3: Nrhiav Ib puag ncig ntawm Ib Daim Duab Peb Hlis Tsis Txaus Siv Txoj Cai ntawm Cosine
Kauj Ruam 1. Kawm Txoj Cai ntawm Cosines
Txoj cai ntawm cosines tso cai rau koj los daws cov teeb meem peb tog thaum koj tsuas paub ob sab qhov ntev thiab ntsuas ntawm lub kaum sab xis ntawm ob sab. Txoj cai lij choj no tuaj yeem siv rau txhua daim duab peb sab, thiab yog cov qauv siv tau zoo heev. Txoj cai ntawm cosines hais tias rau txhua daim duab peb sab nrog sab a, b, thiab c, nrog lub kaum sab xis A, B, thiab C: c2 = ib2 + b2 2ab cos (C).
Kauj Ruam 2. Ua tibzoo saib koj daim duab peb sab thiab tso cov tsiaj ntawv hloov pauv mus rau hauv seem peb tog
Thawj sab koj paub yuav tsum tau cim raws li a, thiab lub kaum sab xis ntxeev sab raws li A. Qhov thib ob uas koj paub yuav tsum tau cim raws li b; thiab lub kaum sab xis ntxeev sab li B. Lub kaum sab xis uas koj paub yuav tsum tau cim raws li C, thiab sab thib peb, sab koj xav tau los xam kom pom thaj tsam ntawm daim duab peb sab, zoo li c.
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Piv txwv, xav txog daim duab peb sab nrog sab 10 thiab 12, thiab lub kaum sab xis nruab nrab ntawm lawv yog 97 °. Peb yuav nkag mus rau qhov hloov pauv raws li hauv qab no: ib = 10, b = 12 hli, C = 97 °.
Kauj Ruam 3. Plug qhov tseem ceeb uas koj paub rau hauv cov mis thiab daws kom tau txais tus nqi c
Ua ntej koj yuav tsum nrhiav lub xwmfab ntawm a thiab b, thiab ntxiv lawv ua ke. Tom qab ntawd, nrhiav tus lej cosine ntawm C siv "cos" ua haujlwm ntawm koj lub laij lej, lossis tus lej cosine online. Muab tus nqi sib npaug cov (C) nrog tus nqi 2 aw ab thiab rho tawm qhov tshwm sim los ntawm qhov sib npaug ntawm a2 + b2. qhov tshwm sim yog tus nqi c2. Nrhiav cov hauv paus plaub ntawm tus nqi no thiab koj yuav tau txais sab ntev c. Siv peb daim duab piv txwv piv txwv:
- c2 = 102 + 122 2 × 10 × 12 × cos (97).
- c2 = 100 + 144 – (240 × -0, 12187) (Hloov tus nqi cosine rau tus lej nrog 5 tus lej zauv.)
- c2 = 244 – (-29, 25)
- c2 = 244 + 29, 25 (Khaws nqa lub cim rho tawm yog tias qhov tshwm sim ntawm cos (C) tsis zoo!)
- c2 = 273, 25
- c = 16, 53 ib
Kauj Ruam 4. Siv sab c txhawm rau nrhiav thaj tsam ntawm daim duab peb sab
Nco qab tias puag ncig ntawm daim duab peb sab yog K = ib + b + c, yog li txhua yam koj yuav tsum tau ua yog ntxiv qhov ntev koj nyuam qhuav tau txais, uas yog sab c nrog paub sab ntev, i.e a thiab b. Yog li yooj yim!
