Ayini ama-engeli aseduze: incazelo, i-theorem, izakhiwo

Kulolu shicilelo, sizocubungula ukuthi ayini ama-engeli aseduze, sinikeze ukwakheka kwe-theorem ephathelene nawo (kuhlanganise nemiphumela evela kuyo), futhi sibhale izici ze-trigonometric zama-engeli aseduze.

Incazelo yamakhona ancikene

Ama-engeli amabili ancikene akha umugqa oqondile nezinhlangothi zawo zangaphandle abizwa eduze. Emfanekisweni ongezansi, lawa amakhona α и β.

Uma amakhona amabili ehlanganyela i-vertex efanayo nohlangothi, anjalo eduze. Kulokhu, izifunda zangaphakathi zalawa makhona akufanele ziphambane.

Umgomo wokwakha ikhona eliseduze

Sinweba enye yezinhlangothi zekhoneni ngokusebenzisa i-vertex ngokuqhubekayo, ngenxa yalokho kwakhiwa ikhoneni elisha, eliseduze nelokuqala.

Ithiyori ye-engeli eseduze

Isamba samadigri ama-engeli aseduze ngu-180°.

Ikhona eliseduze 1 + I-engeli eseduze 2 = 180°

Isibonelo se-1

Enye yama-engeli aseduze ingu-92°, ithini enye?

Isixazululo, ngokusho kwethiyori okukhulunywe ngayo ngenhla, sisobala:

I-engeli eseduze 2 = 180° – I-engeli eseduze 1 = 180° – 92° = 88°.

Impendulo esuka ku theorem:

• Ama-engeli aseduze ama-engeli amabili alinganayo ayalingana elinye.
• Uma i-engeli iseduze ne-engeli engakwesokudla (90°), iphinde ibe ngu-90°.
• Uma i-engeli iseduze ne-acute, khona-ke inkulu kuno-90°, okungukuthi iyisimungulu (futhi ngokuphambene nalokho).

Isibonelo se-2

Ake sithi sine-engeli encikene no-75°. Kumelwe ibe nkulu kuno-90°. Ake sikuhlole.

Ngokusebenzisa i-theorem, sithola inani le-engeli yesibili:

180° – 75° = 105°.

105° > 90°, yingakho i-engeli iyi-obtuse.

Izici ze-Trigonometric zama-engeli aseduze

1. Imisipha yama-engeli ancikene iyalingana, okungukuthi isono α = isono β.
2. Amanani ama-cosine nama-tangents ama-engeli aseduze ayalingana, kodwa anezimpawu eziphambene (ngaphandle kwamanani angachazwanga).
   • cos α = -cos β.
   • tg α = -tg β.