Ko e tapatolu tuliki-tapafā ko e fōtunga ʻaonga taha ʻi he ngāue ʻo e tufunga — ko e fakaholo ʻo e ʻato kotoa pē, ko e pou kotoa pē ʻo e hala-fāʻele, ko e fau fakahalafohi kotoa pē, ko e tipi miter kotoa pē, ko e siʻate fakatapafā kotoa pē ko ha tapatolu tuliki-tapafā ia kuo fakafoliga ʻi ha ngaahi lea kehekehe. Hokohoko mo e ngaahi felekeu tafaʻaki-ʻe-tolu tuliki-ʻe-tolu pea ʻe mole ʻa e tokolahi ʻo e matematika ʻi he feituʻu ngāue. ʻOku fai ʻe he kalakuleita tapatolu ʻa Chippy Tools ʻa e trig mo e Pythagoras maʻáu ʻi he metuliki pe imipealiale — hū ha ongo fika pea ʻe foki mai ʻe he ʻepi ʻa e ngaahi tafaʻaki, tuliki, lahi, mo e takatakai ʻoku mole.
Ko e hā ʻoku fai ʻe he kalakuleita tapatolu
ʻOku fakaleleiʻi ʻe he kalakuleita tapatolu ʻa Chippy Tools ha faʻahinga tapatolu tuliki-tapafā mei ha ongo fika ʻoku ʻiloʻi. ʻE lava ke ʻave ki ai ha ongo tafaʻaki, ha tafaʻaki ʻe taha mo ha tuliki siʻi taha ʻe taha, pe ko ha ongo tuliki (ʻa ia ʻoku fakapauʻi ai ʻa e tuliki ʻe tolu kotoa neongo ʻoku ʻikai ʻiloʻi ʻa e tafaʻaki hono tolu kae ʻoua kuo ʻomi ha tafaʻaki). ʻOku kau ʻi he ngaahi ola ʻa e tafaʻaki ʻe tolu kotoa, tuliki ʻe tolu kotoa, lahi, mo e takatakai. ʻOku fakakau ʻe he kalakuleita tatau pē ʻa e tapatolu makehe 45-45-90 tafaʻaki-tatau tuliki-tapafā, ʻa e tapatolu 30-60-90, mo ha faʻahinga tapatolu tuliki-tapafā masani ʻi he vahaʻa.
ʻOku ngāue ʻa e ʻepi fakalokolo ʻi he iOS mo Android taʻe ha ʻinitaneti. Sui ʻi he vahaʻa ʻo e metuliki mo e imipealiale taʻe ha toe kamata pea fakatolonga ha ngaahi fokotuʻutuʻu masani ʻo e tapatolu (siaki tafatusa ʻo e tuliki 45-45-90, fokotuʻu hex 30-60-90, ngaahi fakaholo masani ʻo e ʻato ko e ngaahi tapatolu) ko ha presets kapau ʻokú ke faʻa ngāueʻaki kinautolu.
Sino ʻo ha tapatolu tuliki-tapafā
ʻOku ʻi ai ʻi he tapatolu tuliki-tapafā ʻa e tafaʻaki ʻe tolu mo e tuliki ʻe tolu. ʻOku 90° maʻu pē ʻa e tuliki ʻe taha (ko e tuliki tapafā); ko e ongo tuliki kehe ko e tuliki siʻi (ʻi lalo ʻi he 90°) pea ʻokú na tānaki ki he 90°. Ko e ongo tafaʻaki ʻokú na fakatupu ʻa e tuliki tapafā ʻoku ui ko e ongo vaʻe (ʻi he taimi ʻe niʻihi ko e “tafaʻaki a” mo e “tafaʻaki b”, pe ko e felāveʻi mo e ofi ʻo fakatatau ki he tuliki ʻokú ke kalakuleita mei ai). Ko e tafaʻaki hono tolu, ʻoku felāveʻi mo e tuliki tapafā, ko e hypotenuse — ko e tafaʻaki loloa taha maʻu pē.
ʻI he fakatātā: (1) tafaʻaki a, (2) tafaʻaki b, (3) hypotenuse, (4) tuliki tapafā, (5) tuliki siʻi.
ʻOku liliu siʻisiʻi ʻa e ngaahi lea ʻi he taimi ʻokú ke fakahā ai ʻa e tuliki ʻokú ke ngāue mei ai. Ki ha tuliki siʻi θ, ko e tafaʻaki felāveʻi ʻoku tuʻu fakahangatonu mei he θ, ko e tafaʻaki ofi ko e vaʻe ʻoku ofi ki he θ (kae ʻikai ko e hypotenuse), pea ʻoku tuʻu pē ʻa e hypotenuse ko e hypotenuse. ʻOku fakamatalaʻi ʻa e ngaahi fēʻunga trigonometric ko e sine, cosine, mo e tangent mei he tafaʻaki ʻe tolu ko ʻeni ʻo fakatatau ki he θ.
ʻE anga fēfē hono lau ʻo e ngaahi tafaʻaki ʻo ha tapatolu tuliki-tapafā
ʻOku ʻomai ʻe he tuʻutuʻuni ʻa Pythagoras ha faʻahinga tafaʻaki pē mei he ongo tafaʻaki kehe:
- hypotenuse = √(tafaʻaki a² + tafaʻaki b²)
- tafaʻaki a = √(hypotenuse² − tafaʻaki b²)
- tafaʻaki b = √(hypotenuse² − tafaʻaki a²)
Ki ha fakatātā kuo fai, ko ha tapatolu mo e ongo tafaʻaki ʻe 3 mo e 4 ʻe ʻi ai ha hypotenuse ko e √(9 + 16) = √25 = 5. Ko e tapatolu 3-4-5 angamaheni ko ha siaki tafatusa lelei ʻi he feituʻu ngāue: ʻoku tafatusa ha holisi kapau ʻe fakafetaulaki ha loloa 3-ʻiunite ʻi he tafaʻaki ʻe taha mo ha loloa 4-ʻiunite ʻi he tafaʻaki ʻe taha ʻi ha hala fakahalafohi 5-ʻiunite.
Ki ha fakatātā imipealiale, ko ha teki mo ha hake 6-futa mo ha laka 8-futa ʻe ʻi ai ha hypotenuse tatau-mo-e-pou ko e √(36 + 64) = √100 = futa tonu ʻe 10 — ko e taha kehe ʻo e tolu Pythagorean haohaoa. ʻOku fa’a ʻikai ke fakatupu ʻe he ngaahi fakafuofua moʻoni ʻa e ngaahi fika maʻa; ʻoku foki mai ʻe he kalakuleita tapatolu ʻa Chippy Tools ʻa e tau decimal totonu ki he tonu ko ia ʻokú ke fie maʻu.
ʻE anga fēfē hono lau ʻo e ngaahi tuliki ʻo ha tapatolu tuliki-tapafā
ʻOku fehokotaki ʻe he ngaahi fēʻunga trigonometric ʻe tolu ʻa e tuliki siʻi ʻe taha ki he ua ʻo e tafaʻaki ʻe tolu:
- sin(θ) = felāveʻi / hypotenuse
- cos(θ) = ofi / hypotenuse
- tan(θ) = felāveʻi / ofi
Ke maʻu ha tuliki mei ha ongo tafaʻaki, ngāueʻaki ʻa e ngaahi fēʻunga fakafoki: arcsin, arccos, pe arctan. Ki ha tapatolu 3-4-5, ko e tuliki ʻoku felāveʻi mo e tafaʻaki ko e loloa 3 ko e arctan(3/4) ≈ 36.87°. Ko e tuliki ʻoku felāveʻi mo e tafaʻaki ko e loloa 4 ko e arctan(4/3) ≈ 53.13°. ʻOku tānaki ʻa e ongo tuliki siʻi ki he 90° maʻu pē: 36.87 + 53.13 = 90 ✓.
ʻOku foki otomeitiki ʻe Chippy Tools ʻa e tuliki ʻe tolu kotoa mei ha ongo tafaʻaki ʻoku ʻiloʻi — ʻoku ʻikai fie maʻu ke manatuʻi pe ko e fē fēʻunga trigonometric ʻoku ngāue ki he fē tuliki.
Lau ʻa e Ngaahi Tapatolu ʻi he Feituʻu Ngāue
Download ʻa Chippy Tools pea ngāueʻaki ʻa e kalakuleita tapatolu ʻi he iOS pe Android. ʻI he taʻe ʻinitaneti, vave, mo tonu — ʻoku ʻikai fie maʻu ha fakaʻiloa ke fokotuʻu ha ʻato, fakatafatusaʻi ha holisi, pe maʻu ha tuliki miter.
Ngaahi tapatolu tafaʻaki-tatau tuliki-tapafā (45-45-90)
Ko e tapatolu 45-45-90 ko e tapatolu makehe tuliki-tapafā angamaheni taha ʻi he ngāue ʻo e tufunga. ʻOku tatau ʻa e ongo vaʻe, ʻoku 45° fakatouʻosi ʻa e tuliki siʻi, pea ʻoku tatau tonu ʻa e hypotenuse mo e vaʻe × √2 ≈ 1.414 × vaʻe. Ko ia ko ha loki tafatusa mo e holisi 4-mita ʻe ʻi ai ha laine tuliki-ki-tuliki ko e 4 × √2 ≈ 5.66m. ʻOku fakahā foki ʻe he 45-45-90 ha faʻahinga tipi miter 45° pē — ʻoku fakatupu ʻe he mata ʻo e tipi ha 45-45-90 mo e tafaʻaki ʻo e laupapa.
Ki he ngaahi tapatolu masani tafaʻaki-tatau (taʻe tuliki-tapafā) — ko ha ongo tafaʻaki tatau ʻokú na fakafetaulaki ʻi ha tuliki ʻulu ʻoku ʻikai 90° — ko e founga ke tuku ha laine fakatuʻu mei he ʻulu ki he tefito. ʻOku vaheua ai ʻa e tafaʻaki-tatau ki ha ongo tapatolu tuliki-tapafā fakasioʻata, ʻa ia ʻe lava ke fakaleleiʻi taki taha ʻe he kalakuleita tapatolu ʻa Chippy Tools.
Ngaahi tapatolu 30-60-90
ʻOku ʻi ai ʻi he 30-60-90 ʻa e ngaahi tuliki 30°, 60°, mo e 90° pea mo e ngaahi fika ʻo e tafaʻaki ko e 1 : √3 : 2. Kapau ko e tafaʻaki ʻoku felāveʻi mo e tuliki 30° ko e ʻiunite ʻe 1, ko e tafaʻaki ʻoku felāveʻi mo e tuliki 60° ko e √3 ≈ 1.732 ngaahi ʻiunite, pea ʻoku tatau tonu ʻa e hypotenuse mo e ʻiunite ʻe 2. ʻOku hā ʻa e tapatolu ko ʻeni ʻi he ngaahi fokotuʻu hex, ʻi he fakatataa ʻo e tuliki ʻo e ʻato hip, mo ha faʻahinga ngāueʻaki pē ʻoku puleʻi ai ʻe he ngaahi tuliki 60°.
ʻOku ʻikai fakamālohia ʻe he kalakuleita ʻa Chippy Tools ʻa e ngaahi fakafuofua makehe — ʻokú ke hū ha ongo fika pea ʻe foki mai ʻa e fika hono tolu. Ko e fakafuofua 1 : √3 : 2 ko ha siaki ʻaonga ki he ola, ka ʻoku tokangaʻi ʻe he ʻepi ʻa e matematika ʻo e fika taʻe-fakatatau maʻáu.
Kalakuleita tuliki miter
Ko e tuliki miter ko e vaheua ʻo e tuliki ʻi he vahaʻa ʻo ha mata ʻe ua ʻoku fehoanaki. Ki ha holisi ʻe ua ʻoku fakafetaulaki ʻi ha tuliki tafatusa (90°), ko e tipi miter taki taha ko e 45°. Ki he ngaahi tuliki taʻe-tafatusa — fa’amalama bay, ngaahi holisi langa-fakaleleiʻi taʻe-tafatusa, ngaahi pou hexagonal — ko e tuliki miter ko e (180° − tuliki ʻo e tuliki) / 2. Ko ia ko ha tuliki 120° (masani ki he hex) ʻe ʻomai ai ha miter ko e (180 − 120) / 2 = 30° ʻi he konga taki taha.
Ki he ngaahi miter fakatuʻufaʻatasia (crown molding, ʻa ia ʻoku nofo ʻa e moulding ʻi ha tuliki spring mei he holisi), ʻoku lavea ange ʻa e matematika — ʻokú ke fie maʻu ʻa e tuliki miter mo ha tuliki bevel. ʻOku tokangaʻi hangatonu ʻe he kalakuleita tapatolu ʻa Chippy Tools ʻa e miter faingofua. Ki he ngaahi miter fakatuʻufaʻatasia ʻo e crown-moulding, fokotuʻu ʻa e tapatolu tuliki-tapafā ʻo e foliga ʻo e moulding pea lau ʻa e tuliki mei he ʻulu.
Ngaahi ngāueʻaki angamaheni: ʻato, hala-fāʻele, teki, miter
ʻOku fakaivia ʻe he ngaahi tapatolu tuliki-tapafā ʻa e tokolahi ʻo e ngaahi lau ʻo e tufunga:
- Fakaholo ʻo e ʻato — ko e hake-ki-he-laka ko ha tapatolu tuliki-tapafā; ko e ʻakau ko e hypotenuse. Vakai ki he Kalakuleita Fakaholo ʻo e ʻAto ki he ngāue makehe.
- Pou ʻo e hala-fāʻele — ʻoku fakatupu ʻe he hake kātoa mo e laka kātoa ha tapatolu tuliki-tapafā; ko e pou ko e hypotenuse. Vakai ki he Kalakuleita Sitepu.
- Ngaahi laine ʻo e teki — ʻoku ngāueʻaki ʻa e Pythagoras ʻi hono fakatafatusaʻi ʻo ha teki pe tefito: ko ha tolu 3-4-5 (pe 6-8-10, 9-12-15) ʻe fakamoʻoniʻi ʻa e tafatusa. Vakai ki he Kalakuleita Siaki Tafatusa.
- Ngaahi tipi miter — ko e miter taki taha ko ha palopalema tapatolu tuliki-tapafā ia kuo fakafoliga ko ha palopalema tuliki.
- ʻAkau hip — ko e ʻakau hip ko ha tapatolu tuliki-tapafā ko e laka ko e laine fakahalafohi ʻo e fua ʻafe ʻo e plan ʻo e fale.
- Ngaahi tipi fau — ko e ngaahi fau fakahalafohi ʻi he faʻunga ko e ngaahi hypotenuse ʻo e tapatolu tuliki-tapafā kuo fua ke fenāpasi ʻi he vahaʻa ʻo e ongo stud ʻe ua.
ʻOku tuʻutuʻuni fakataha ʻa e kalakuleita tapatolu ʻi he ʻepi ʻo Chippy Tools tatau mo e ngaahi kalakuleita makehe ʻo e Fakaholo ʻo e ʻAto, Sitepu, mo e Siaki Tafatusa — kamata mo e founga pē ʻoku fenāpasi mo e ngāue pea hifo ki he kalakuleita tapatolu masani ki ha faʻahinga palopalema fakaheometelika makehe pē.
Matematika ʻo e Tapatolu ʻOku Ne Ngāue Pē
ʻOku tokangaʻi ʻe Chippy Tools ʻa e ngaahi tapatolu tuliki-tapafā, fakaholo ʻo e ʻato, pou ʻo e hala-fāʻele, fokotuʻu ʻo e decking, mo e ngaahi vaheʻangā ʻo e balustrade ʻi he ʻepi pē ʻe taha. Download ʻi he taimi ʻe taha, lau ʻi ha feituʻu pē — ʻoku ʻikai fie maʻu ha ʻinitaneti.
Ngaahi ʻiunite imipealiale mo metuliki
ʻOku tali ʻe Chippy Tools ʻa e milimita, sentimita, mita, futa, ʻinisi, pe ko e futa mo e ʻinisi ʻi ha tuʻunga pē. Hū ʻa e tafaʻaki ʻe taha ʻi he ʻinisi mo e tafaʻaki ʻe taha ʻi he mita kapau ʻoku haʻu hoʻo ngaahi hū mei ha ngaahi maʻuʻanga felākasi — ʻoku liliu ʻe he ʻepi ʻi loto pea ʻoku foki mai ʻa e ngaahi tafaʻaki ʻi hoʻo ʻiunite ʻokú ke saʻi ai. ʻOku ʻi he tikilī maʻu pē ʻa e ngaahi tuliki ʻi he tukunga ʻuluʻulu mo e fili ke sui ki he radians ki he ngaahi ngāue inisinia.
ʻOku ʻikai ha ʻiunite ʻo e ngaahi felāveʻi ʻo e tapatolu ʻi honau fōtunga maʻa (Pythagoras, sin/cos/tan) — ʻoku tuʻu kinautolu ki ha faʻahinga ʻiunite tutuʻu pē. ʻOku tokangaʻi ʻe he kalakuleita ʻa Chippy Tools ʻa e liliu ʻo e ʻiunite koeʻuhí ke ke lava ʻo fefiloi ʻa e ngaahi hū imipealiale mo metuliki ʻi he lau tatau pē taʻe ha fehālaaki.
Ko e hā ʻokú ke ngāueʻaki ai ha kalakuleita tapatolu ʻi hoʻo telefoni
ʻOku langa ʻa e ʻepi ʻa Chippy Tools ki he kau ngāue ʻa ia ʻoku fie maʻu ha lau ʻi he feituʻu ngāue taʻe ha ʻinitaneti. ʻOku tuʻutuʻuni fakataha ʻa e kalakuleita tapatolu mo e Kalakuleita Fakaholo ʻo e ʻAto, Kalakuleita Sitepu, Kalakuleita Siaki Tafatusa, mo e Kalakuleita Decking — lau ha ʻakau hip, ha pou ʻo e hala-fāʻele, ha laine ʻo e teki, mo ha tipi miter ʻi ha founga pē ʻe taha taʻe ha toe hū ʻo e ngaahi fua.
ʻOku maumau ʻa e ngaahi kalakuleita tapatolu ʻi he ʻinitaneti ʻi he ngaahi fale ʻi lalo ʻo e kelekele taʻe ha fakaʻiloa pea ʻi he ngaahi feituʻu langa-foʻou mamaʻo ʻoku siʻi ai ʻa e 4G. ʻOku ngāue fakalokolo ʻa e kalakuleita ʻa Chippy Tools — ʻoku ʻi he matavavae ʻa e tali ʻi lalo ʻi he sēkoni ʻe taha. Sui ʻi he vahaʻa ʻo e sin/cos/tan taʻe fakakaukau pe ko e fē ʻoku ngāue, pea toho hake ʻa e kalakuleita hangatonu mei hoʻo widget ʻi he matavavae ʻo e ʻapi ʻi he taimi ʻoku kole ai ʻe ha kasitomā ha fika vave ʻi he taimi ʻo e kuotaina."
Ngaahi kalakuleita felāveʻi
- Kalakuleita Fakaholo ʻo e ʻAto — matematika tatau ʻo e tapatolu tuliki-tapafā ʻoku tefito ki he ngaahi ʻakau mo e fakaholo ʻo e ʻato
- Kalakuleita Sitepu — matematika tatau ʻo e tapatolu tuliki-tapafā ʻoku tefito ki he ngaahi pou ʻo e hala-fāʻele
- Kalakuleita Siaki Tafatusa — siaki ʻo e laine fakatatau ki he Pythagoras ki he ngaahi tefito, teki, mo e holisi
- Kalakuleita Decking — ki he ngaahi fakafuofua ʻo e teki ʻa ia ʻoku hū ai ʻa e ngaahi laine ʻo e tapatolu tuliki-tapafā