Nā waiwai kiʻekiʻe o ka huinakolu ʻākau

Ma kēia hoʻolaha, e noʻonoʻo mākou i nā waiwai nui o ke kiʻekiʻe ma kahi triangle kūpono, a me ka nānā ʻana i nā hiʻohiʻona o ka hoʻoponopono ʻana i nā pilikia ma kēia kumuhana.

'Ōlelo Aʻo: kapaia ka huinakolu mika'ākau, ina ua pololei kekahi o kona mau kihi (e like me 90°) a o na aoao elua he oi (<90°).

Nā waiwai kiʻekiʻe ma ka huinakolu ʻākau

Waiwai 1

ʻElua mau kiʻekiʻe o ka huinakolu ʻākau (h₁ и h₂) kulike me kona mau wawae.

ʻekolu kiʻekiʻe (h₃) iho i ka hypotenuse mai kahi kihi ʻākau.

Waiwai 2

Aia ke kikowaena orthocenter (kahi o ka hui ana o na kiekie) o ka huinakolu kupono ma ka piko o ka huina kupono.

Waiwai 3

ʻO ke kiʻekiʻe o ka huinakolu ʻākau i kaha ʻia i ka hypotenuse e puʻunaue i ʻelua huinakolu ʻākau like, a ua like pū me ka huinakolu mua.

1. △US ~ △ABC ma na huina like elua: ∠ADB = ∠LAC (laina pololei), ∠US = ∠ʻAmelisa.

2. △ADC ~ △ABC ma na huina like elua: ∠ADC = ∠LAC (laina pololei), ∠CDA = ∠ACB.

3. △US ~ △ADC ma na huina like elua: ∠US = ∠DAC, ∠hewa = ∠CDA.

Hōʻike: ∠hewa = 90° – ∠ABC (ABC). Ma ka manawa like ∠ACD (ACB) = 90° – ∠ABC.

No laila, ∠hewa = ∠CDA.

Hiki ke hooiaioia ma ke ano like me ∠US = ∠DAC.

Waiwai 4

Ma ka huinakolu kupono, ua heluia ke kiekie i hukiia i ka hypotenuse penei:

1. Ma o na mahele ma ka hypotenuse, i hanaia mamuli o kona mahele ana ma ke kumu o ke kiekie:

2. Ma na loa o na aoao o ka huinakolu.

Loaʻa kēia ʻano kumu mai ʻO nā ʻano o ka sine o kahi kihi acute ma ka huinakolu pololei (ua like ka sine o ka huina me ka ratio o ka wawae ku e me ka hypotenuse):

'Ōlelo Aʻo: i kahi huinakolu kūpono, nā waiwai kiʻekiʻe maʻamau i hōʻike ʻia ma kā mākou hoʻolaha - pili pū kekahi.

Laʻana o kahi pilikia

Hana 1

Ua māhele ʻia ka hypotenuse o kahi huinakolu ʻākau e ke kiʻekiʻe i huki ʻia iā ia i mau ʻāpana 5 a me 13 knm. E huli i ka lōʻihi o kēia kiʻekiʻe.

pāʻoihana

E hoʻohana kākou i ke ʻano kumu mua i hōʻike ʻia ma Waiwai 4:

Hana 2

ʻO nā wāwae o ka huinakolu ʻākau he 9 a me 12 knm. E huli i ka lōʻihi o ke kiʻekiʻe i kaha ʻia i ka hypotenuse.

pāʻoihana

ʻO ka mua, e ʻimi kākou i ka lōʻihi o ka hypotenuse (e waiho i nā wāwae o ka huinakolu "I" и "B", a o ka hypotenuse “vs”):

c² =A² + b² = 9² + 12² = 225.

ʻO ke kumu iho, ʻo с = 15 knm.

I kēia manawa hiki iā mākou ke hoʻohana i ke ʻano lua mai Waiwai 4i kūkākūkā ʻia ma luna: