Yadda za a sami hypotenuse wata dama alwatika

Daga cikin da yawa lissafin sanya ga lissafi na daban-daban yawa na daban-daban na lissafi siffofi, an gano da hypotenuse na alwatika. Ka tuna cewa a alwatika aka kira wani polyhedron da ciwon uku kusassari. Kasa ne a 'yan hanyoyi daban-daban da yin lissafi da hypotenuse na triangles za a ba.

Da farko, bari mu ga yadda za a samu hypotenuse wata dama alwatika. Ga waɗanda m, da ake kira rectangular alwatika da ciwon wani kwana na 90 digiri. gefe na alwatika, located a kan kishiyar sashi na dama kwana da ake kira hypotenuse. Bugu da kari, shi ne mafi tsawo gefe na alwatika. Dangane da tsawon na hypotenuse san yawa da aka lasafta kamar haka:

• Known tsawon kafafu. Hypotenuse a wannan harka da aka lasafta ta yin amfani da Pythagorean Theorem, wanda ya karanta kamar haka: square na hypotenuse daidai da Naira Miliyan Xari da murabba'ai na sauran bangarorin biyu. Idan muka yi la'akari da dama-angled alwatika BKF, inda BK da KF da kafafu da kuma FB - da hypotenuse, da FB2 = BK2 + KF2. Yana bi da cewa a kirga tsawon na hypotenuse kamata a tashe alternately a kowane daga cikin square dabi'u na sauran bangarorin biyu. Sa'an nan kuma ƙara sama da lambobin da cewa dauka da sakamakon da square tushen.

Ka yi la'akari da wannan misali: Dan alwatika da dama kwana. Daya kafa ne 3 cm, 4 cm wani. Nemo hypotenuse. The bayani ne kamar haka.

FB2 = BK2 + KF2 = (3cm) 2+ (4 cm) 2 = + 9sm2 16sm2 = 25 cm2. Mu cire square tushen da kuma samun FB = 5cm.

• Known cathetus (BK) da kwana dab da shi, wanda Forms da hypotenuse da kuma cewa kafa. Yadda za a sami hypotenuse na alwatika? Mun nuna a fakaice da aka sani kwana α. Bisa ga dukiya daga wani rectangular alwatika, wanda ya ce da rabo daga kafar tsawon zuwa tsawon na hypotenuse ne daidaita da cosine na kwana tsakanin hypotenuse da kafa. Ganin wannan alwatika za a iya rubuta kamar: FB = BK * cos (α).
• Known cathetus (KF) da kuma daidai da kwana α, kawai yanzu ya za a tsaurin. Yadda za a sami hypotenuse a cikin wannan hali? Bari mu duk da wannan Properties na da hakkin alwatika kuma mun koyi cewa rabo daga kafar tsawon zuwa tsawon na hypotenuse ne daidaita da ba tare da na kwana na da sabani gefe. Wannan shi ne, FB = KF * zunubi (α).

La'akari da wadannan misali. Ba duka guda-dama angled alwatika da hypotenuse BKF FB. Bari kwana F daidai digiri 30, na biyu kwana B ne 60 digiri. Wani da aka sani cathetus BK, da tsawon wanda yayi dace 8 cm lissafta da ake so darajar a matsayin yiwu .:

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

• Known da'irar radius (R), ya bayyana game da alwatika da dama kwana. Yadda za a sami hypotenuse a cikin shawara da irin wannan matsala? Daga cikin kaddarorin da da'irar circumscribing da alwatika da dama kwana da aka sani, irin wannan cewa cibiyar daga cikin da'irar yi daidai da aya daga cikin hypotenuse rarraba shi a cikin rabin. A sauki kalmomi - radius yayi dace da rabi na hypotenuse. Saboda haka, hypotenuse ne daidai sau biyu da radius. FB = 2 * R. Idan ba a irin wannan matsalar, wanda ba a san radius, da kuma tsakãtsaki ce, ya kamata ka kula da dukiya daga cikin da'irar circumscribed game da alwatika da dama kwana, cewa ya ce radius ne daidaita da tsakãtsaki ce kõma zuwa ga hypotenuse. Amfani da duk wadannan kaddarorin, matsalar da aka warware su a cikin hanyar.

Idan tambaya shi ne yadda za a sami hypotenuse na wani isosceles dama alwatika, shi wajibi ne a tuntube duk da wannan Pythagorean Theorem. Amma, da farko na dukkan tuna cewa isosceles alwatika ne alwatika cewa yana da biyu daidaita bangarorin biyu. A cikin hali na da hakkin alwatika daidai tarnaƙi ne kafafu. Da FB2 = BK2 + KF2, amma kamar yadda BK = KF mun da wadannan: FB2 = 2 BK2, FB = BK√2

Kamar yadda ka gani, sanin Pythagorean Theorem da kaddarorin a dama alwatika, don magance matsalar da kuke bukatar yin lissafi da tsawon hypotenuse, shi ne mai sauqi qwarai. Idan duk da kaddarorin wuya a tuna, koyi shirye-sanya dabarbari, musanya a san dabi'u a cikin abin da zai yiwu yin lissafi da ake bukata tsawon na hypotenuse.