Kodi kupeza hypotenuse wa kansalu bwino

Pakati kuwerengetsera ambiri anapanga mawerengedwe a zedi zosiyanasiyana zosiyanasiyana akalumikidzidwa zojambula, ndi kupeza hypotenuse wa makona lapansi. Kumbukirani kuti kansalu amatchedwa polyhedron ndi kumathandiza kupeza ngodya zitatu. Pansipa pali njira zochepa zosiyana kuwerengera hypotenuse wa Triangles adzapatsidwa.

Poyamba, tiyeni tiwone momwe kupeza hypotenuse wa kansalu bwino. Anthu dzimbiri, wotchedwa amakona anayi makona ndi makona a madigiri 90. mbali ya makona ndi, inali mbali ina ya mlingo woyenerera amatchedwa hypotenuse. Komanso, ndi mbali yaitali kwambiri makona lapansi. Malinga ndi kutalika kwa hypotenuse kudziwika zedi kuchita masamu motere:

• Mumadziwika kutalika kwa miyendo. Hypotenuse Pankhaniyi kuchita masamu ntchito Lingaliro Lovomerezeka Pythagorean, lomwe limati motere: lalikulu la hypotenuse ndi wofanana Uwerenge mabwalo mbali zina ziwiri. Ngati tikambirana ufulu-angled makona BKF, kumene BK ndi KF miyendo ndi FB - ndi hypotenuse, ndi FB2 = BK2 + KF2. Ndizoonekeratu kuti kuwerengetsa kutalika kwa hypotenuse ayenera adzaukitsidwa alternately aliyense mfundo lalikulu la mbali zina ziwiri. Kenaka yikani manambala ndi kuti anatengedwa ndi zotsatira za muzu lalikulu.

Taganizirani chitsanzo ichi: Dan makona ndi mlingo woyenerera. mwendo umodzi ndi 3 cm, 4 cm wina. Pezani hypotenuse. Yankho motere.

FB2 = BK2 + KF2 = (3cm) 2+ (4 cm) 2 = + 9sm2 16sm2 = 25 cm2. Ife wachotsa lalikulu mizu ndi kupeza FB = 5cm.

• Mumadziwika cathetus (BK) ndi ngodya pafupi izo, imene imagwiritsidwa ntchito hypotenuse ndi kuti mwendo. Kodi kupeza hypotenuse wa makona ya? Ife potanthauza kudziwika ngodya α. Malinga ndi chuma cha kansalu amakona anayi, amene amanena kuti chiŵerengero cha kutalika mwendo ndi kutalika kwa hypotenuse ndi wofanana ndi cosine ya njingayo pakati pa hypotenuse ndi mwendo. Poganizira makona uyu akhoza kulembedwa monga: FB = BK * Ko (α).
• Mumadziwika cathetus (KF) ndi chimodzimodzi α njingayo, okha tsopano izi kuti otsutsanawa. Kodi kupeza hypotenuse mu nkhani iyi? Tiyeni ife tonse katundu womwewo wa makona bwino ndipo timaphunzira kuti chiŵerengero cha kutalika mwendo ndi kutalika kwa hypotenuse ndi wofanana ndi sine a mbali ya mbali ina. Ndiko kuti, FB = KF machimo (α).

Taganizirani chitsanzo chotsatirachi. Popeza onse womwewo-angled makona ndi hypotenuse BKF FB. Tiyeni mbali F liri madigiri 30, wachiwiri ngodya B ndi madigiri 60. Wina cathetus kudziwika BK, kutalika kwa Chofanana masentimita 8 kugwira ntchito zowerengetsa mtengo wolakalakika ngati n'kotheka .:

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

• Mumadziwika bwalo utali wozungulira (R), anafotokoza za kansalu ndi mlingo woyenerera. Kodi kupeza hypotenuse mu kulingalira ngati vuto? Kuchokera katundu wa bwalo circumscribing ndi makona ndi mlingo woyenerera amadziwika, kotero likulu la bwalo chikugwirizana ndi mfundo za hypotenuse nagawira mu theka. Mu mawu osavuta - utali wozungulira wa limafanana ndi theka la hypotenuse lapansi. Choncho, hypotenuse ndi wofanana ndi kawiri utali wozungulira wa. FB = 2 * R. Ngati anapatsidwa nayenso, amene samadziwika utali wozungulira, ndi apakatikati, muyenera khutu ku chuma cha bwalo circumscribed za makona ndi mlingo woyenerera, amene amanena kuti utali wozungulira ndi wofanana ndi apakatikati kukopeka hypotenuse lapansi. Kugwiritsa onse katundu awa, vutoli kuthetsedwa chimodzimodzi.

Ngati funso ndi momwe kupeza hypotenuse ya isosceles makona bwino, m'pofunika kufufuza anthu onse kwa chomwecho Pythagorean Lingaliro Lovomerezeka. Koma, poyamba pa zonse kumbukirani kuti makona isosceles ndi kansalu kuti ali awiri mbali ofanana. Pankhani ya kansalu bwino mbali ofanana ndi miyendo. Ndi FB2 = BK2 + KF2, koma monga BK = KF ife zotsatirazi: FB2 = 2 BK2, FB = BK√2

Monga mukuonera, podziwa Lingaliro Lovomerezeka Pythagorean ndi katundu wa kansalu lamanja, kuthetsa vuto limene muyenera kuwerengera kutalika hypotenuse, ndi lophweka. Ngati katundu onse zimandivuta kukumbukira, kuphunzira okonzeka zopangidwa mitunduyi, m'malo mfundo yodziwika imene zidzakhala zosatheka kuwerengetsa kutalika ofunikira hypotenuse lapansi.