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Kalkuleta na Alwatika na Dama

Gefen da kusurwoyin alwatika na dama da suka ɓace daga ƙafafunsa biyu - hypotenuse, kusurwoyi, yanki, da kewaye.

Ƙara zuwa wurin aiki

Ƙimomin shigarwa

Gefen biyu suna haɗuwa a kusurwar dama. Duk tsayi a cikin na'ura ɗaya. Sakamako suna sabuntawa yayin da kuke rubutu. Duk lissafin suna gudana a gida a cikin burauzar ku.

Hypotenuse

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Kusurwoyi: —Yanki: —Gefen: —

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Ƙa’ida

Pythagoras: hypotenuse c = √(a² + b²). Kusurwoyi masu kaifi suna fitowa daga gefuna: kusurwar da ke gaban ƙafar a shine arctan(a ÷ b), kuma kusurwar da ke gaban ƙafar b shine 90° a rage wannan kusurwar - kusurwoyi masu kaifi biyu koyaushe suna ƙarawa zuwa 90°. Yanki = ½ × a × b, da kewaye = a + b + c.

Misalin aiki

Kafafu 3 da 4: hypotenuse = √(3² + 4²) = √25 = 5. Kusurwar da ke gaban gefen 3 ita ce arctan(3 ÷ 4) = 36.87°, don haka ɗayan kusurwar mai tsanani ita ce 90 − 36.87 = 53.13°. Yanki = ½ × 3 × 4 = 6, da kuma kewaye = 3 + 4 + 5 = 12. Alwatika na 3–4–5 shine ƙaramin alwatika na dama tare da gefuna masu lambobi gaba ɗaya, shi ya sa yake bayyana ko'ina daga wuraren gini zuwa matsalolin littafin karatu.

Amfani da iyakoki

Wannan shafin yana ɗaukar ƙafafu biyu na alwatika na dama. Ba ya warware alwatika idan aka ba da hypotenuse da ƙafa ɗaya, ko kuma idan aka ba da kusurwa da gefe - ga waɗannan, yi amfani da Pythagoras ko trigonometry kai tsaye akan dabarar da ke sama. Yana ɗauka cewa kusurwar da ke tsakanin ɓangarorin biyu da aka shigar daidai ne 90°; Ga kowace alwatika, waɗannan dabarun ba sa aiki. Kusurwoyi suna nunawa a digiri zuwa digiri biyu.

Sigar tsari: f0697a60d4c3 · An duba misali:

FAQ

Me yasa a² + b² = c²?

Ka'idar Pythagoras ce: a cikin alwatika ta dama, murabba'in da aka gina akan hypotenuse yana da yanki iri ɗaya da murabba'ai biyu da aka gina akan ƙafafu a haɗe. Yana riƙe da kowace alwatika ta dama, ba kawai lambobi gaba ɗaya ba.

Menene alwatika ta 3–4–5?

Mafi ƙarancin alwatika ta dama tare da gefuna na lambobi gaba ɗaya: 3² + 4² = 9 + 16 = 25 = 5². Masu ginin sun yi amfani da igiyoyi masu ƙulli a cikin rabon 3–4–5 tsawon shekaru aru-aru don shimfida kusurwoyin dama daidai, tunda duk wani mai yawa (6–8–10, 9–12–15) yana aiki iri ɗaya.

Ta yaya ake samun kusurwoyin?

Daga rabon ƙafafu: kusurwoyin da ke gaban ƙafa a ya cika tan(kusurwoyi) = a ÷ b, don haka kusurwa = arctan(a ÷ b). Kusurwoyin da ke da ƙarfi na biyu shine 90° ban da na farko ba, saboda jimlar kusurwoyin alwatika zuwa 180° kuma kusurwar dama ta riga ta ɗauki 90°.

Zan iya shigar da hypotenuse maimakon ƙafa?

Ba a wannan shafin ba — yana tsammanin ƙafafu biyu. Idan kun san hypotenuse c da ƙafa ɗaya a, ɗayan ƙafar ita ce √(c² − a²), wanda za ku iya ƙididdigewa sannan ku shigar a nan.

Shin raka'o'in suna da mahimmanci?

Sai dai cewa ƙafafu biyu suna amfani da raka'a ɗaya: hypotenuse, yanki, da kewaye sannan su fito a cikin wannan raka'a da murabba'inta. Haɗa mita da santimita yana ba da amsa mara kyau, don haka fara juyawa.

Yaya game da alwatika marasa dama?

Pythagoras ba ya aiki. Alwatika gabaɗaya suna buƙatar dokar cosines (c² = a² + b² − 2ab·cos C) ko dabarar Heron ta mai lissafin yanki na alwatika, ya danganta da abin da kuka sani.

Kayan aiki masu alaƙa

Sakamako kimantawa ne kawai kuma ba ya nufin shawarar ƙwararru.