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Azungezwe unxantathu: umqondo, izici, izindlela sokunquma

Triangle ingenye bobunjwa eziyisisekelo weJiyomethri emelela ezintathu intersecting umugqa izingxenye. Lesi sibalo ukuthi isazi waseGibhithe lasendulo, eGreece yasendulo futhi China owanikhipha iningi amafomula amaphethini ezisetshenziswa ososayensi, onjiniyela kanye nabaqambi kuze kube manje eyaziwa.

The main ingxenye izingxenye unxantathu yilezi:

• isiqongo - iphuzu empambana izingxenye.

• Amaphathi - intersecting umugqa izingxenye.

Ngokusekelwe kulezi izingxenye, bahlanganise imiqondo ezifana azungezwe unxantathu, endaweni yayo, kuqoshwe nemibuthano circumscribed. Kusukela esikoleni siyazi ukuthi azungezwe unxantathu luwukubonakaliswa zezinombolo yesamba zonke ezintathu ezinhlangothini zalo. Ngesikhathi esifanayo amafomula lokuthola le value abaningi eyaziwa, kuncike idatha yoqobo ukuthi abacwaningi endabeni ethile.

1. Indlela elula ukuthola azungezwe unxantathu isetshenziswa endabeni lapho amanani ezinombolo baziwa yonke ezintathu ezinhlangothini zalo (x, y, z), njengoba phetho:

P = x + y + z

2. azungezwe unxantathu equilateral zingatholakala, uma sikhumbula ukuthi lesi sibalo wonke amaphathi Nokho, njengoba zonke engele bayalingana. Ukwazi ubude eceleni i equilateral unxantathu ipherimitha ibalwa kanje:

P = 3x

3. isosceles calantsatfu, ngokungafani equilateral, izinhlangothi ezimbili kuphela kwenani elifanayo zezinombolo, Nokho kulesi simo azungezwe ifomu jikelele kuyoba kanje:

P = 2x + y

4. Izindlela ezilandelayo zibalulekile ezimweni lapho amanani ezinombolo eyaziwa akuzona zonke izinhlangothi. Ngokwesibonelo, uma isifundo idatha ezinhlangothini ezimbili, eyaziwa engela therebetween, azungezwe unxantathu zingatholakala nangokunquma wesithathu kanye engela ezaziwayo. Kulokhu, lo wesithathu kuyotholakala kusukela ifomula:

z = 2x + 2y-2xycosβ

Ngakho, azungezwe unxantathu ilingana:

P = x + y + 2x + (2y-2xycos β)

5. Esimweni lapho ubude ekuqaleni unikezwa hhayi okungaphezu kokukodwa uhlangothi unxantathu kanye eyaziwa amanani ezinombolo we-engeli amabili naso eduze, azungezwe unxantathu ingabalwa ngesisekelo theorem sine:

P = x + sinβ x / (isono (180 ° -β)) + sinγ x / (isono (180 ° -γ))

6. Kukhona amacala lapho ukuthola azungezwe unxantathu usebenzisa eyaziwa imingcele umbuthano elalibhalwe therein. Lokhu ifomula Kuyaziwa ukuba iningi namanje esikoleni:

P = 2S / r (S - endaweni embuthanweni, kuyilapho r - engaba).

Kusukela zonke lezi zindlela osekukhulunywe kuyacaca ukuthi ukubaluleka azungezwe unxantathu zingatholakala ngezindlela eziningi, ngesisekelo idatha aphethwe umcwaningi. Ngaphezu kwalokho, kukhona ezimbalwa ezimweni ezikhethekile, ukuthola leli nani. Ngakho, azungezwe ingenye ezibaluleke kakhulu kanye nezici unxantathu kwesokudla angled.

Njengoba yaziwa, ukuze ngokuthi unxantathu ukuma, izinhlangothi ezimbili akha engela kwesokudla. Azungezwe unxantathu kwesokudla yinani lika inkulumo ezinombolo ngokusebenzisa kokubili imilenze kanye hypotenuse. Kuleso simo, uma umcwaningi eyaziwa idatha kuphela ezinhlangothini ezimbili, okusele ingabalwa usebenzisa theorem kaPythagoras owaziwa: z = (x2 + y2), uma yaziwa, kokubili umlenze, noma x = (Z2 - y2), uma hypotenuse nasemlenzeni ezaziwayo.

Kuleso simo, uma sazi ubude hypotenuse umuntukazana eduze we ngasemagumbini alo, ezinye izinhlangothi ezimbili onikeza: x = z sinβ, y = z cosβ. Kulokhu, azungezwe unxantathu kwesokudla ilingana:

P = z (cosβ + sinβ +1)

Futhi, uma kwenzeka olukhethekile ukubala azungezwe lesifanele (noma equilateral) unxantathu, okungukuthi, abe semqoka kangaka lapho zonke izinhlangothi futhi zonke engele bayalingana. Ukubalwa azungezwe unxantathu kuthabathela ecaleni eyaziwa akunankinga, Nokho, abacwaningi ngokuvamile ukwazi ezinye idatha. Ngakho, uma engaba eyaziwayo emjikelezweni olotshiwe, azungezwe unxantathu njalo enikezwa:

P = 6√3r

Uma unikezwa ukubaluleka engaba umbuthano circumscribed, i equilateral unxantathu ipherimitha kutholakala ngendlela elandelayo:

P = 3√3R

Amafomula kudingeka khumbula priment ngempumelelo practice.

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