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 (lossis vertex). Feem ntau txoj hauv kev los ntsuas cov ces kaum yog qib, nrog rau lub voj voos ntsuas 360 degrees. Koj tuaj yeem suav qhov ntsuas ntawm lub kaum sab xis hauv lub duab plaub yog tias koj paub cov duab ntawm lub ntsej muag thiab ntsuas ntawm nws lwm lub ces kaum lossis, hauv qhov xwm txheej ntawm daim duab peb sab, yog tias koj paub ntsuas ob ntawm nws ob sab. Ib qho ntxiv, koj tuaj yeem ntsuas cov ces kaum siv tus kws txiav txim plaub lossis xam lub kaum sab xis yam tsis muaj tus kws txiav txim plaub siv lub tshuab xam zauv.
Cov kauj ruam
Txoj Kev 1 ntawm 2: Xam Cov Sab Hauv Sab Hauv Polygon
Kauj Ruam 1. Suav tus naj npawb ntawm ob sab hauv cov duab
Txhawm rau xam cov ces kaum sab hauv ntawm lub duab plaub, koj yuav tsum xub txiav txim siab tias muaj pes tsawg sab uas muaj ntau lub duab. Nco ntsoov tias lub polygon muaj tus lej zoo ib yam li nws muaj cov ces kaum.
Piv txwv li, daim duab peb sab muaj 3 sab thiab 3 sab hauv sab thaum lub xwmfab muaj 4 sab thiab 4 lub kaum sab hauv
Kauj Ruam 2. Nrhiav qhov ntsuas tag nrho ntawm tag nrho cov ces kaum sab hauv hauv cov duab
Cov mis rau nrhiav qhov ntsuas tag nrho ntawm txhua lub ces kaum sab hauv hauv ib lub duab plaub yog: (n - 2) x 180. Hauv qhov no, n yog tus lej ntawm ob sab uas lub duab plaub muaj. Qee qhov kev ntsuas ntau lub kaum sab xis ntsuas yog raws li hauv qab no:
- Cov ces kaum hauv daim duab peb sab (3-sided polygon) tag nrho 180 degrees.
- Cov ces kaum nyob rau hauv ib lub xwmfab plaub fab (4-sided polygon) tag nrho 360 degrees.
- Cov ces kaum hauv lub pentagon (5-sided polygon) tag nrho 540 degrees.
- Cov ces kaum hauv lub hexagon (6-sided polygon) tag nrho 720 degrees.
- Cov ces kaum nyob rau hauv lub octagon (8-sided polygon) tag nrho 1080 degrees.
Kauj Ruam 3. Faib qhov ntsuas tag nrho ntawm txhua lub polygon lub kaum ntse ntse los ntawm tus lej ntawm nws cov ces kaum
Ib lub duab plaub tsis tu ncua yog lub duab plaub uas nws sab yog txhua qhov ntev thiab nws cov ces kaum muaj qhov ntsuas tib 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 xis 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 ntau, thaum Pentagon hauv Washington, DC yog piv txwv ntawm lub tsev pentagon tsis tu ncua thiab daim paib nres yog piv txwv ntawm lub kaum hli ib txwm muaj
Kauj Ruam 4. Rho tawm qhov suav ntawm cov ces kaum uas paub los ntawm kev ntsuas tag nrho ntawm cov ces kaum rau cov duab tsis xwm yeem
Yog tias koj lub polygon tsis muaj ob sab ntawm tib qhov ntev thiab cov ces kaum ntawm qhov ntsuas tib yam, txhua yam koj yuav tsum tau ua yog ntxiv tag nrho cov kev paub hauv cov ces kaum. Tom qab ntawd, rho tus lej ntawd los ntawm kev ntsuas tag nrho ntawm txhua lub ces kaum kom pom lub kaum uas ploj lawm.
Piv txwv li, yog tias koj paub tias 4 ntawm cov ces kaum hauv lub pentagon ntsuas 80, 100, 120, thiab 140 degrees, ntxiv cov lej ua ke kom tau txais cov lej ntawm 440. Tom qab ntawd, rho tawm qhov suav no los ntawm qhov ntsuas tag nrho rau lub pentagon, uas yog 540 degrees: 540 - 440 = 100 degrees. Yog li, lub kaum sab xis uas ploj lawm yog 100 degrees
Tswv yim:
Qee lub tebchaws muaj "cheats" los pab koj txheeb xyuas qhov ntsuas ntawm qhov tsis paub. Ib daim duab peb sab isosceles yog daim duab peb sab nrog 2 sab ntawm qhov ntev sib npaug thiab 2 lub kaum sab xis ntawm kev ntsuas sib npaug. Ib daim duab plaub sib npaug yog plaub fab plaub fab nrog ob sab sib npaug ntawm qhov sib npaug thiab cov ces kaum kab pheeb ces kaum sib txawv ntawm qhov ntsuas sib npaug.
Txoj Kev 2 ntawm 2: Nrhiav Cov Kaum Nyob Hauv Ib Daim Duab Peb Hlis
Kauj Ruam 1. Nco ntsoov tias txhua daim duab peb sab xis muaj ib lub kaum sab xis sib npaug 90 degrees
Los ntawm kev txhais, daim duab peb sab txoj cai ib txwm muaj ib lub kaum sab xis uas yog 90 degrees, txawm tias nws tsis sau npe li ntawd. Yog li, koj yuav ib txwm paub tsawg kawg ib lub kaum ntse ntse thiab tuaj yeem siv trigonometry los nrhiav lwm 2 lub kaum ntse ntse.
Kauj Ruam 2. Ntsuas qhov ntev ntawm 2 ntawm daim duab peb sab
Qhov ntev tshaj plaws ntawm daim duab peb sab hu ua "hypotenuse." Sab "nyob ib sab" nyob ib sab (lossis ib sab ntawm) rau lub kaum sab xis uas koj tab tom txiav txim siab. Sab "rov qab" yog qhov rov qab rau lub kaum sab xis koj tab tom sim txiav txim siab. Ntsuas 2 ntawm ob sab kom koj tuaj yeem txiav txim siab ntsuas ntawm cov ces kaum uas seem hauv daim duab peb sab.
Tswv yim:
Koj tuaj yeem siv lub tshuab xam zauv los daws koj cov kab zauv lossis nrhiav lub rooj online uas teev cov txiaj ntsig rau ntau yam sine, cosine, thiab tangent ua haujlwm.
Kauj Ruam 3. Siv qhov sine muaj nuj nqi yog tias koj paub qhov ntev ntawm sab nraud thiab hypotenuse
Ntsuas koj qhov txiaj ntsig rau qhov kev ua zauv: sine (x) = rov qab ÷ hypotenuse. Hais tias qhov ntev ntawm sab nraud yog 5 thiab qhov ntev ntawm hypotenuse yog 10. Sib faib 5 los 10, uas yog sib npaug 0.5. Tam sim no koj paub tias sine (x) = 0.5 uas zoo ib yam li x = sine-1 (0.5).
Yog tias koj muaj lub tshuab xam zauv, tsuas yog ntaus 0.5 thiab nias sine-1. Yog tias koj tsis muaj lub tshuab xam zauv, siv daim duab online los nrhiav tus nqi. Ob leeg yuav qhia tias x = 30 degrees.
Kauj Ruam 4. Siv lub cosine muaj nuj nqi yog tias koj paub qhov ntev ntawm ib sab uas nyob ib sab thiab qhov hypotenuse
Rau hom teeb meem no, siv kab zauv: cosine (x) = nyob ib sab ÷ hypotenuse. Yog tias qhov ntev ntawm sab uas nyob ib 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).
Plug 0.833 rau hauv koj lub tshuab xam zauv thiab nias cosine-1. Xwb, saib tus nqi hauv daim duab cosine. Cov lus teb yog 33.6 degrees.
Kauj Ruam 5. Siv txoj haujlwm tangent yog tias koj paub qhov ntev ntawm sab nraud thiab sab uas nyob ib sab
Qhov sib npaug rau kev ua haujlwm tangent yog tangent (x) = rov qab ÷ nyob ib sab. Hais tias koj paub qhov ntev ntawm sab nraud yog 75 thiab qhov ntev ntawm sab uas nyob ib sab yog 100. Sib faib 75 los ntawm 100, uas yog 0.75. Qhov no txhais tau tias tangent (x) = 0.75, uas yog tib yam li x = tangent-1 (0.75).
Nrhiav tus nqi hauv daim duab tangent lossis nias 0.75 ntawm koj lub tshuab xam zauv, tom qab ntawd tangent-1. Qhov no yog sib npaug rau 36.9 degrees.
Lub tswv yim
- Cov ces kaum tau muab cov npe raws li ntau qib lawv ntsuas. Raws li tau hais los saud, lub kaum sab xis ntsuas 90 degrees. Lub kaum sab xis ntsuas ntau dua 0 tab sis tsawg dua 90 degrees yog lub kaum ntse ntse. Lub kaum sab xis ntsuas ntau dua 90 tab sis tsawg dua 180 degrees yog lub kaum obtuse. Lub kaum sab xis ntsuas 180 degrees yog lub kaum ncaj, thaum lub kaum sab xis ntsuas ntau dua 180 degrees yog lub kaum sab xis.
- Ob lub kaum sab xis uas ntsuas ntsuas mus txog 90 degrees hu ua lub kaum ntxiv. (Ob lub kaum sab xis uas tsis yog lub kaum sab xis hauv daim duab peb sab yog lub kaum sab xis ntxiv.) Ob lub kaum sab xis uas ntsuas ntsuas mus txog 180 degrees hu ua cov ces kaum ntxiv.
