Hauv geometry, lub kaum sab xis yog qhov chaw nruab nrab ntawm 2 txoj kab hluav taws xob (lossis ntu ntu) nrog tib qhov kawg (aka vertex). Txoj hauv kev feem ntau los ntsuas cov ces kaum yog siv qib, thiab lub voj voog puv muaj lub kaum sab xis ntawm 360 degrees. Koj tuaj yeem suav qhov ntsuas ntawm ib lub kaum sab xis hauv ib lub duab plaub yog tias koj paub cov duab ntawm lub ntsej muag thiab ntsuas ntawm lwm lub ces kaum, lossis hauv qhov xwm txheej ntawm daim duab peb sab, yog tias koj paub qhov ntev ntawm ob sab. Ib qho ntxiv, koj tuaj yeem ntsuas cov ces kaum uas siv lub arc lossis suav lawv siv lub tshuab xam zauv.
Kauj ruam
Txoj Kev 1 ntawm 2: Xam Sab Hauv Sab Ntawm Lub Polygon
Kauj Ruam 1. Suav tus naj npawb ntawm ob sab hauv cov duab
Yuav kom xam lub kaum sab xis sab hauv ntawm lub duab plaub, koj xub yuav tsum txiav txim siab tias muaj pes tsawg sab uas cov duab muaj. Paub tias tus naj npawb ntawm ob sab ntawm lub polygon sib npaug rau qhov sib npaug ntawm nws cov ces kaum.
Piv txwv li, daim duab peb sab muaj 3 sab thiab 3 lub kaum sab hauv, thaum lub xwmfab muaj 4 sab thiab 4 lub kaum sab hauv
Kauj Ruam 2. Nrhiav tag nrho qhov loj me ntawm txhua lub kaum sab hauv ntawm lub polygon
Cov mis rau nrhiav qhov loj me ntawm txhua lub ces kaum hauv ib lub duab plaub yog: (n - 2) x 180. Hauv qhov no, n yog tus lej ntawm ob sab uas muaj ntau lub duab plaub. Tag nrho lub kaum sab xis qhov ntau thiab tsawg hauv qee cov duab ntau yog raws li hauv qab no:
- Tag nrho cov ces kaum hauv ib daim duab peb sab (3 tog polygon) yog 180 degrees.
- Tag nrho cov ces kaum hauv cov plaub fab (4-sided polygon) yog 360 degrees.
- Tag nrho cov ces kaum hauv lub pentagon (5-sided polygon) yog 540 degrees.
- Tag nrho cov ces kaum hauv lub hexagon (6-sided polygon) yog 720 degrees.
- Tag nrho cov ces kaum hauv daim duab peb sab (7-sided polygon) yog 1080 degrees.
Kauj Ruam 3. Sib faib tag nrho lub kaum sab xis me me ntawm txhua lub polygons li niaj zaus los ntawm cov lej ntawm lawv cov ces kaum
Ib lub duab plaub tsis tu ncua yog lub duab plaub uas nws txhua sab yog tib qhov ntev, yog li txhua lub ces kaum zoo ib yam. Piv txwv li, qhov ntsuas ntawm txhua lub kaum sab xis hauv daim duab peb sab sib npaug yog 180 3, lossis 60 degrees, thiab ntsuas ntawm txhua lub kaum sab hauv ib lub xwmfab yog 360 4, lossis 90 degrees.
Cov vajvoos peb sab sib luag thiab cov duab plaub yog cov piv txwv ntawm cov duab ntau zaus, thaum Pentagon hauv Washington, DC, Tebchaws Asmeskas, yog piv txwv ntawm pentagons tsis tu ncua, thiab nres cov cim yog piv txwv ntawm cov octagons tsis tu ncua
Kauj Ruam 4. Rho tawm tag nrho cov kev ntsuas lub kaum sab xis los ntawm qhov sib npaug ntawm txhua lub kaum ntse ntse uas paub los nrhiav qhov ntsuas ntawm cov ces kaum hauv cov duab tsis xwm yeem
Yog tias cov duab tsis muaj tib sab ntev thiab ntsuas lub kaum sab xis, koj tsuas yog xav tau ntxiv txhua qhov kev paub hauv lub kaum sab xis. Tom qab ntawd, rho tawm tag nrho lub kaum sab xis ntsuas ntawm cov duab sib txuas los ntawm cov lej ntawm txhua lub kaum ntse ntse uas paub los nrhiav qhov ntsuas ntawm lub kaum sab xis uas tsis paub.
Piv txwv li, yog tias koj paub tias 4 lub kaum sab xis hauv lub pentagon yog 80, 100, 120, thiab 140 degrees feem, ntxiv lawv kom tau 440. Tom qab ntawd, rho tus lej ntawd los ntawm tag nrho lub kaum sab xis ntsuas ntawm lub pentagon, uas yog 540 degrees: 540 - 440 = 100 degrees. Yog li, lub kaum sab xis ntxiv yog 100 degrees
Tswv yim:
Qee lub tebchaws muaj "luv" los pab koj ntsuas lub kaum ntse ntse uas tsis paub. Ib daim duab peb sab isosceles yog daim duab peb sab uas muaj ob sab sib npaug thiab 2 lub kaum sib npaug sib npaug. Ib daim duab plaub sib npaug yog plaub fab plaub fab nrog tib qhov ntev ntawm ob sab sib npaug thiab ntsuas tib yam ntawm kab pheeb ces kaum sib txawv.
Txoj Kev 2 ntawm 2: Nrhiav Lub Kaum Nyob Hauv Ib Daim Duab Peb Hlis
Kauj Ruam 1. Nco ntsoov tias hauv txhua daim duab peb sab sab xis tsuas muaj ib lub kaum sab xis uas sib npaug 90 degrees
Los ntawm kev txhais, lub kaum sab xis ib txwm muaj qhov ntsuas sib npaug 90 degrees, txawm tias nws tsis sau npe. Yog li koj yuav ib txwm paub qhov ntsuas ntawm tsawg kawg ib lub kaum ntse ntse thiab tuaj yeem siv trigonometry los nrhiav qhov ntsuas ntawm lwm ob lub kaum ntse ntse.
Kauj Ruam 2. Ntsuas qhov ntev ntawm ob sab ntawm daim duab peb sab
Qhov ntev tshaj plaws ntawm daim duab peb sab hu ua "hypotenuse." Sab "sab" yog sab ntawm lub kaum sab xis uas koj xav pom qhov loj ntawm. Sab "pem hauv ntej" yog sab sab lub kaum sab xis uas koj tab tom nrhiav. Ntsuas ob sab no kom koj tuaj yeem txiav txim siab qhov loj ntawm cov ces kaum uas seem hauv daim duab peb sab.
Tswv yim:
Koj tuaj yeem siv lub tshuab xam zauv los daws qhov sib npaug lossis saib hauv online cov npe uas teev cov txiaj ntsig ntawm ntau yam sine, cosine, thiab tangent.
Kauj Ruam 3. Siv txoj haujlwm sine yog tias koj paub qhov ntev ntawm sab thiab qhov hypotenuse
Ntsuas cov lej rau hauv kab zauv: sine (x) = pem hauv ntej hypotenuse. Hais qhov ntev ntawm sab nraud yog 5 thiab qhov ntev ntawm hypotenuse yog 10. Sib faib 5 nrog 10, uas yog sib npaug 0.5. Tam sim no koj paub tias sine (x) = 0.5, uas yog sib npaug rau x = sine-1 (0, 5).
Yog tias koj muaj lub tshuab xam zauv, tsuas yog ntaus hauv 0.5 thiab nias sine-1. Yog tias koj tsis muaj lub tshuab xam zauv, siv daim duab online los nrhiav tus nqi. Koj yuav pom tias x = 30 degrees
Kauj Ruam 4. Siv txoj haujlwm cosine yog tias koj paub qhov ntev ntawm sab thiab qhov hypotenuse
Txog cov teeb meem zoo li no, siv qhov sib npaug: cosine (x) = sab hypotenuse. Yog hais tias qhov ntev ntawm sab yog 1.666 thiab qhov ntev ntawm hypotenuse yog 2.0, faib 1.666 los ntawm 2, uas yog sib npaug rau 0.833. Yog li, cosine (x) = 0.833 lossis x = cosine-1 (0, 833).
Sau 0.833 rau hauv lub tshuab xam zauv thiab nias tus lej cosine-1. Txwv tsis pub, saib daim duab qhia nqi cosine. Cov lus teb yog 33.6 degrees.
Kauj Ruam 5. Siv lub luag haujlwm tangent yog tias koj paub qhov ntev ntawm sab xub ntiag thiab sab
Qhov sib npaug rau txoj haujlwm tangent yog tangent (x) = sab xub ntiag. Hais tias koj paub qhov ntev ntawm sab xub ntiag yog 75 thiab sab ntev yog 100. Sib faib 75 los ntawm 100, uas yog 0.75. Ntawd yog, tangent (x) = 0.75, uas yog tib yam li x = tangent-1 (0, 75).
Saib tus nqi hauv daim duab tangent lossis nias 0.75 ntawm lub tshuab xam zauv, tom qab ntawd tangent-1. Nws tus nqi sib npaug rau 36.9 degrees.
Lub tswv yim
- Cov ces kaum muaj npe raws li lawv qhov loj me. Raws li tau hais los saum no, lub kaum sab xis yog ntsuas ntawm 90 degrees. Lub kaum sab xis uas tsawg dua 90 tab sis ntau dua 0 degrees hu ua lub kaum ntse ntse. Lub kaum sab xis uas nws ntsuas ntau dua 90 degrees thiab tsawg dua 180 degrees hu ua obtuse kaum. Cov ces kaum uas ntsuas 180 degrees yog hu ua lub kaum ncaj, thaum lub kaum sab xis siab dua 180 degrees yog hu ua lub kaum ntse ntse.
- Ob lub kaum uas ntxiv mus txog 90 degrees yog hu ua lub kaum ntxiv (ob lub kaum sab xis uas tsis yog lub kaum sab xis hauv txoj cai daim duab peb sab yog cov ces kaum sib ntxiv). Ob lub kaum uas ntxiv rau 180 degrees hu ua cov ces kaum ntxiv.
