Pehea e loaʻa i ka hypotenuse o ka triangle akau

Mawaena o na ho lehulehu i no ka i ka ho omaulia ana o kekahi mau mea o okoa geometric ano, ua loaa i ka hypotenuse o ka triangle. Keia iloko o i ua kapaia he triangle he polyhedron ka ekolu pana pua. Aia ma lalo nō he mauʻano likeʻole, e hoʻomaulia i ka hypotenuse o na triangle mauna e e haawiia mai.

Initially, e ka ike pehea e loaʻa i ka hypotenuse o ka triangle akau. No ka poe Malama Ka, i kapa mau huinahń triangle me ka huina o ka 90 degere. ʻaoʻao o ka triangle, Aia ma kaʻaoʻao e ku pono ana o ka huina akau ua kapaia ka hypotenuse. Eia hou, ka mea, o kaʻaoʻao loihi o ka triangle. Ke kaumaha ma muli o ka lōʻihi o ka hypotenuse ikeia puuhuahelu he pōpilikia like penei:

• Ike lōʻihi o nā wāwae. Hypotenuse ma keia hihia he pōpilikia ka hoʻohana 'ana i ka Pythagorean theorem, i heluhelu like penei: lākou, kū pono ana i ka hypotenuse ka huina o na mika pāhoʻonui lua o ka mea'ē aʻe nāʻaoʻaoʻelua. Inā mākou e noonoo i ka pono-huina triangle BKF, kahi BK a me KF na wawae a me FB - ka hypotenuse, ke FB2 = BK2 + KF2. Ua penei i ka helu ana i ka lōʻihi o ka hypotenuse E e hoalaia mai alternately ma kela a me keia o na huinahalike aiee o ka'ē aʻe nāʻaoʻaoʻelua. A laila, hui mai i ka helu, a ua laweʻia e ka hopena o ka huinahalike kumu.

E hoomanao i keia hana: Dana triangle me ka huina akau. Kekahi wāwae He 3 knm, 4 knm kekahi. E huli i ka hypotenuse. Ke kākoʻo pāʻoihana Ua like penei.

FB2 = BK2 + KF2 = (3cm) 2+ (4 knm) 2 = + 9sm2 16sm2 = 25 cm2. Mākou extract ka huinahalike kumu , ae lawe FB = 5cm.

• Ike cathetus (BK) a me ka huina e pili ia ia, i konaʻano a ka hypotenuse, a i ka wawae. Pehea e loaʻa i ka hypotenuse o ka triangle? Mākou Kû ka ike huina α. E like me ka waiwai o ka huinahń triangle, i mai nei i ka lākiō o ka wāwae lōʻihi a hiki i ka lōʻihi o ka hypotenuse mea like me ka cosine o ka huina ma waena o ka hypotenuse, a me ka uha mua. E noonoo pono i keia triangle hiki ke palapalaia e like me: FB = BK * cos (α).
• Ike cathetus (KF) a me ka huina α, wale kēia manawa ka mea, ua e kue. Pehea e loaʻa i ka hypotenuse ma keia hihia? E iā mākou a pau i ka mea waiwai o ka triangle'ākau, a me ke aʻo ana i ka lākiō o ka wāwae lōʻihi a hiki i ka lōʻihi o ka hypotenuse mea like me ka sine o ka huina o kaʻaoʻao e keʻakeʻa i. Ia mea, FB = KF * hewa (α).

ke kēia kumu noonoo. Ua haawiia i ka mea pono-huina triangle me ka hypotenuse BKF FB. E ka huina F lākou, 30 degere, i ka lua o ka huina B ka 60 degere. Kekahi ike cathetus BK, ka lōʻihi o ka i hoʻopili like i 8 knm Compute i ka makemake waiwai like hiki .:

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

• Ike kaiapili kahahńnai (R), i ho'ākāka 'ia e pili ana i ka triangle me ka huina akau. Pehea e loaʻa i ka hypotenuse ma ka noonoo ana o ia i ka pilikia? Mai ka waiwai o ka p ÷ ai circumscribing ka triangle me ka huina akau ua ikeia, e like ana ka piko o ka p ÷ ai coincides me ka wahi o ka hypotenuse mahele ia i ka hapalua o. Ma na mea hua'ōlelo - ke kahahńnai o hoʻopili like no ka hapalua o ka hypotenuse. Nolaila, ke hypotenuse mea like i palua ka kahahńnai. FB = 2 * R. Inā i hāʻawi i ka like pilikia, i ua ole ike kahahńnai, a me ka Media, oe e hoʻolohe i ka waiwai o ka p ÷ ai circumscribed e pili ana i ka triangle me ka huina akau, i mai nei i ke kahahńnai o ka poepoe like a hiki i ka Media e holo pololei a hiki i ka hypotenuse. E ho ohana a pau o kēia mau waiwai, o ka pilikia ua Wehewehe i nā hāʻina ma ka ia ala.

Inā ka ninau mea ana e imi i ka hypotenuse o ka isosceles pono triangle, ia mea pono e kelepona a pau i ka mea hookahi Pythagorean theorem. Akā, mua o nā mea a pau e hoomanao i ka isosceles triangle mea he triangle e loaʻa mau likeʻaoʻaoʻelua. Ma ka hihia o ka triangle pono likeʻaoʻao i nā wāwae. Ua FB2 = BK2 + KF2, akā, me BK = KF mākou i nā kēia: FB2 = 2 BK2, FB = BK√2

Me oe e ike, e ike ana i ka Pythagorean theorem, a me ka waiwai o ka triangle akau, e hoʻoponopono i ka pilikia no ka a au pono e hoʻomaulia i ka lōʻihi o ka hypotenuse, ka mea, o loa mea. Inā na ka waiwai a pau o ka hana, e hoomanao, aʻo hoomakaukau-i nā papakuhikuhi, hookomoia i ike Hawaiʻi ma i mea e e hiki, e hoʻomaulia i ka koi loa o ka hypotenuse.