Indlela yokuthola azungezwe unxantathu?

Indlela yokuthola azungezwe unxantathu? Ngakho ebuzwa lo mbuzo ngamunye wethu, esikoleni. Ake sizame ukukhumbula konke esikwaziyo lesi sibalo emangalisayo, kanye ukuphendula umbuzo.

Impendulo yombuzo kanjani ukuthola azungezwe unxantathu ngokuvamile ulula - kuthatha kuphela-nje ulandele inqubo ukwengeza ubude zonke izinhlangothi zalo. Nokho, zikhona izindlela ezimbalwa ezilula ubuningi engaziwa.

amathiphu

Kuleso simo, uma engaba (r) circle olotshwe unxantathu, kanye endaweni yayo (S) zaziwa, impendulo yombuzo kanjani ukuthola azungezwe unxantathu oluphakeme elula. Ukuze wenze lokhu, udinga ukusebenzisa ifomula evamile:

P = 2S / r

Uma ama-engeli zaziwa, isibonelo, α futhi β, okuyizinto eduze kuze kube sohlangothini uqobo futhi ohlangothini obuphelele, azungezwe zingatholwa kusetshenziswa ifomula kakhulu, ethandwa kakhulu okungukuthi:

sinβ ∙ a / (isono (180 ° - β - α)) + sinα ∙ a / (isono (180 ° - β - α)) + a

Uma ulazi ubude emaceleni ezisondele kanye β engela, okuyinto phakathi kwawo, ukuze uthole azungezwe ke, kuyadingeka ukusebenzisa theorem ka cosines. Azungezwe ibalwa kanje:

P = b + a + √ (B2 + A2 - 2 ∙ b ∙ kanye ∙ cosβ),

lapho A2 kanye B2 kukhona izigcawu ubude izinhlangothi eduze. Inkulumo Radical - ubude kowesithathu alwaziwa, kuphawulwa theorem cosine.

Uma ungazi kanjani ukuba uthole azungezwe of unxantathu isosceles, lapha, eqinisweni, akunandaba ngempela. Bala usebenzisa ifomula:

P = b + 2a,

lapho b - kumila unxantathu, futhi - ezinhlangothini zalo.

Ukuze uthole azungezwe unxantathu equilateral kufanele usebenzise ifomula elula:

R = 3a,

nalapho - ubude eceleni.

Indlela yokuthola azungezwe unxantathu uma sazi kuphela radii emibuthano echazwe ngayo noma bangena kuyo? Uma unxantathu kuyinto equilateral, khona-ke kufanele sisebenzise ifomula:

P = 3R√3 = 6r√3,

lapho R r kukhona radii kwendilinga circumscribed futhi angabhalwa ngokulandelana.

Uma unxantathu kuyinto isosceles ke ifomula kusebenza kuye:

P = 2R (sinβ + 2sinα),

lapho α - iyi-engela elisemandleni ngasesinqeni, futhi β - i-engeli okuyinto obuhlukile base.

Ngokuvamile, ukuxazulula izinkinga zezibalo ledzinga kuhlatiywa ngokujulile kanye nekhono ethize ukuze uthole futhi sibonise amafomula edingekayo, okuyinto, njengoba abaningi bazi, impela umsebenzi kunzima. Nakuba ezinye izinkinga zingaxazululwa nje ifomula olulodwa.

Ake sicabangele izimpendulo zemibuzo ifomula ukuthi kukhona isisekelo ukuphendula umbuzo kanjani ukuthola azungezwe unxantathu, maqondana Tinhlobo onxantathu.

Yiqiniso, ukubusa esiyinhloko ekutholeni azungezwe unxantathu - la mazwi: kuyadingeka walala ubude ezinhlangothini zalo phezu ifomula ezifanele zokuthola azungezwe unxantathu:

P = b + a + c,

lapho b, a futhi - ubude izinhlangothi unxantathu, futhi P - azungezwe unxantathu.

Kunezinhlobo eziningana amacala olukhethekile ifomula. Ake sithi inkinga yakho zavela ngale ndlela: "kanjani ukuthola ipherimitha unxantathu kwesokudla" Kulokhu, kufanele usebenzise le ndlela elandelayo:

P = b + a + √ (B2 + A2)

Kulesi ifomula, a futhi b kukhona ubude imilenze unxantathu ngokushesha kwesokudla. Kulula ukuqagela ukuthi esikhundleni ohlangothini (hypotenuse) isetshenziswa inkulumo isuselwe theorem omkhulu usosayensi endulo - Pythagoras.

Uma ufuna ukuxazulula inkinga, lapho onxantathu zifana ke kunengqondo ukusebenzisa lesi sitatimende: isilinganiso perimeters we Coefficient okuhambisanayo okufana ngaso. Ake sithi une onxantathu ezimbili ezifanayo - ΔABC futhi ΔA1B1C1. Khona-ke ukuthola isici okufana ngaso ezohlukaniswa azungezwe ΔABC ΔA1B1C1 ipherimitha.

Ekuphetheni, kufanele kuphawulwe ukuthi azungezwe unxantathu ingatholakala kusetshenziswa tinhlobonhlobo temasu, kuye ngokuthi idatha yomthombo ukuthi une. Kumele wanezela ukuthi kukhona ezinye izimo ezikhethekile ukuba onxantathu kwesokudla angled.