Indlela yokuthola hypotenuse unxantathu kwesokudla

Phakathi izibalo eziningi ezihunyushwe sokubalwa eziningi ezihlukahlukene ezahlukene zeJiyomethri, ukuthola hypotenuse unxantathu. Khumbula ukuthi unxantathu ibizwa ngokuthi polyhedron kokuba engeli ezintathu. Ngezansi izindlela ezimbalwa ezahlukene ukubala hypotenuse we onxantathu uzonikezwa.

Ekuqaleni, ake sibone ukuthi ukuthola hypotenuse unxantathu kwesokudla. Kulabo ibuthuntu, okuthiwa unxantathu unxande kokuba i-engela 90 degrees. uhlangothi unxantathu, esisogwini uhlangothi engela kwesokudla ubizwa ngokuthi hypotenuse. Ngaphezu kwalokho, kuyinto ohlangothini olude unxantathu. Kuye ubude hypotenuse eyaziwa nenani ibalwa kanje:

• Ubude Akwaziwa of the imilenze. Hypotenuse kulokhu ubalwa kusetshenziswa theorem kaPythagoras, esifundeka kanje: esigcawini hypotenuse lilingana isamba izigcawu the nezinye izinhlangothi ezimbili. Uma sicabanga ilungelo-angled unxantathu BKF, lapho BK futhi KF kwemilenze FB - the hypotenuse, le FB2 = BK2 + KF2. It kulandela ukuthi ekubaleni ubude hypotenuse kufanele avuswe yanjalo ngamunye amagugu skwele ezinye izinhlangothi ezimbili. Bese wengeza up the izinombolo nokuthi ezithathwe umphumela impande square.

Cabanga ngalesi sibonelo: Dan unxantathu nge engela kwesokudla. Umlenze owodwa 3 cm, 4 cm komunye. Thola hypotenuse. Isixazululo kanje.

FB2 = BK2 + KF2 = (3cm) 2+ (4 cm) 2 = + 9sm2 16sm2 = 25 cm2. Thina kukhishwe isikwele impande futhi uthole FB = 5cm.

• cathetus Akaziwa (BK) kanye engela eseduze nale ndlela, okuyinto yakha hypotenuse nokuthi umlenze. Indlela yokuthola hypotenuse unxantathu? Thina isho engela α ezaziwayo. Ngokusho impahla unxantathu unxande, othi isilinganiso umlenze ngobude ubude hypotenuse ilingana cosine ye-engeli phakathi hypotenuse nomlenze. Ukucabangela lesi unxantathu singatlolwa bunjesi: FB = BK * cos (α).
• cathetus Akaziwa (KF) futhi okufanayo engela α, kuphela manje kumele eziphikisanayo. Indlela yokuthola hypotenuse kulesi simo? Sonke asibambe sezindawo efanayo unxantathu kwesokudla futhi sifunda ukuthi isilinganiso umlenze ngobude ubude hypotenuse uyalingana sine ye-engeli we ophikisayo. Okungukuthi, FB = KF yesono (α).

Cabangela isibonelo esilandelayo. Kuyona inikele konke okufanayo unxantathu wesokudla-yomumo nge hypotenuse BKF FB. Vumela engela F kulingana degrees 30, owesibili engela B degrees 60. Enye cathetus eyaziwa BK, ubude okuhambelana 8 cm ikhompyutha ukubaluleka oyifunayo ngangokunokwenzeka .:

FB = BK / cos60 = 8 cm.
FB = BK / sin30 = 8 cm.

• Akwaziwa umbuthano engaba (R), echazwe mayelana calantsatfu engela kwesokudla. Indlela yokuthola hypotenuse e kuhlolwe inkinga enjalo? Kusukela izakhiwo emjikelezweni onciphisa unxantathu nge engela kwesokudla yaziwa, yokuthi maphakathi umbuthano kuvumelana iphuzu hypotenuse ukukucaza ngesigamu. Ngamagama alula - engaba oluhambisana uhhafu we hypotenuse. Ngakho, hypotenuse ilingana kabili engaba. FB = 2 * R. Uma unikezwa nenkinga efanayo, okuyinto hhayi engaba eyaziwa, futhi imidiyeni, kufanele sinake impahla emjikelezweni circumscribed mayelana unxantathu nge engela kwesokudla, ukuthi uthi engaba ilingana imidiyeni badonsekela hypotenuse. Ukusebenzisa zonke lezi izakhiwo, inkinga isixazululekile ngendlela efanayo.

Uma umbuzo indlela ukuthola hypotenuse i unxantathu isosceles kwesokudla, kubalulekile ukuxhumana bonke theorem efanayo Pythagorean. Kodwa, okokuqala kunakho konke khumbula ukuthi unxantathu isosceles kuyinto unxantathu ukuthi kukabili alinganayo. Endabeni unxantathu kwesokudla amacala alingane kukhona imilenze. Have FB2 = BK2 + KF2, kodwa njengoba BK = KF siye okulandelayo: FB2 = 2 BK2, FB = BK√2

Njengoba ubona, ngokwazi theorem kaPythagoras kanye izakhiwo unxantathu kwesokudla, ukuxazulula inkinga okuyiwona udinga ukubala ubude hypotenuse, silula. Uma zonke izindawo kunzima ukukhumbula, funda amafomula ngomumo eyenziwe, esikhundleni amagugu aziwayo lapho sizokwazi ukubala ubude okwakufuneka hypotenuse.