Selikalikoe le Seqha
Selikalikoe ke se seng sa dibopeho tsa motheo le tse feto-fetohang tsa jeometri. Bophelong ba letsatsi le letsatsi, re bona dilikalikoe ka mefuta e fapaneng, ho tloha diwatjheng tsa lebota le mabili a koloi ho isa ho didikadikwe tsa dipolanete tsamaisong ya letsatsi. Sehloohong sena, re tla hlahloba selikalikoe ka botebo mme re hlahlobe e nngwe ya dikarolo tsa sona tsa bohlokwa: chord.
Tlhaloso ea Selikalikoe
Ho ya ka dipalo, sedikadikwe ke pokello ya dintlha tsohle tse ka hara sefofane tse hole ka ho lekana le ntlha e bohareng e fanweng. Sebaka sena se bitswa radius, mme ntlha e bohareng e bitswa bohareng ba sedikadikwe. Diforomo tsa motheo tsa sedikadikwe (C) le sebaka (A) sa sedikadikwe ke tse latelang:
– Perimithara (C): \[C = 2\pir \]
– Sebaka (A): \[ A = \pi r^2 \]
moo \( r \) e leng radius ea selikalikoe le \( \pi \hoo e ka bang 3.14159 \).
Likarolo tsa Selikalikoe
Ntle le radius le setsi, ho na le likarolo tse ling tse 'maloa tsa bohlokoa ka har'a selikalikoe:
1. Bophara: Mola o otlolohileng o fetang bohareng ba selikalikoe mme o hokahanya dintlha tse pedi selikalikoeng. Thepa e ikgethang ya bophara ke hore bolelele ba yona kamehla bo feta radius habeli: \( D = 2r \).
2. Arc: Karolo ea selikalikoe sa selikalikoe pakeng tsa lintlha tse peli. Arc e ka lekanngoa ka likhato kapa li-radian, ho latela moelelo oo li sebelisitsoeng ho oona.
3. Khoro: Karolo ea mola e hokahanyang lintlha tse peli selikalikoeng. Khoro e fetang bohareng ba selikalikoe e tsejoa e le bophara.
Ho Utloisisa Lithapo tsa Seqha
Chord ke e 'ngoe ea likarolo tse hlokomolohuoang haholo ho geometry e chitja, empa e bapala karolo ea bohlokoa. Chord ke mola o otlolohileng o hokahanyang lintlha tse peli selikalikoeng. Ho fapana le radius kapa bophara, e lulang e feta bohareng ba selikalikoe, chord e ka ba kae kapa kae ha feela lintlha tse peli tseo li li hokahanyang li le moeling oa selikalikoe.
Matlotlo a Lithapo tsa Seqha
1. Bolelele ba khoele ea seqha: Bolelele ba khoele ea seqha bo ka baloa ho sebelisoa mekhoa e 'maloa e fapaneng, ho latela tlhahisoleseling e fanoeng. Foromo e le 'ngoe e tloaelehileng ke:
\[ c = 2 \cdot R \cdot \sin \left( \dfrac{\theta}{2} \right) \]
moo \( c \) e leng bolelele ba chord, \( R \) ke radius, mme \( \theta \) ke sekhutlo se bohareng se bopilweng ke radii tse pedi tse kopanang dintlheng tsa chord.
2. Sebaka ho tloha Bohareng: Khoele e telele e tla ba haufi le bohareng ba selikalikoe ho feta khoele e kgutshwane. Ha e le hantle, khoele e telele ka ho fetisisa selikalikoeng ke bophara ba yona.
3. Ho lekana: Khouto e arola selikalikoe ka dihalofo tse pedi tse lekanang. Haeba re taka mola o otlolohileng ho tloha bohareng ba selikalikoe ho ya khoutong, ntlha ya moo ho kopanang teng e arola khouto ka dihalofo tse pedi tse lekanang.
4. Kamano le Radius: Haeba khoele le radius li etsa khutlotharo, re ka bala bolelele ba khoele le liparamente tse ling re sebelisa metheo ea trigonometry le molao oa li-cosine.
Litšebeliso tsa Seqha Bophelong ba Letsatsi le Letsatsi
1. Boenjiniere le Meaho: Moralong oa meaho le oa meaho, li-chord li sebelisoa ho hlalosa li-curve kapa li-arches ka har'a moaho. Mohlala, borokhong bo nang le li-arched kapa dome.
2. Bolepi ba Dinaledi le Tsamaiso: Bolepi ba Dinaledi, ho balwa ha khoele ya arc ho thusa ho fumana tsela e kgutshwane pakeng tsa dintlha tse pedi hodima lefatshe (sebaka se seholo sa sedikadikwe). Sena se bohlokwa haholo boeping ba difofane le tsamaisong ya tsona.
3. Tšebeliso Moralong: Lithapo tsa seqha hangata li sebelisoa likarolong tse fapaneng tsa moralo, ho tloha litšoantšong, bononong ba pono ho ea fesheneng ho etsa libopeho le lipaterone tse ntle.
Likamano tsa Lipalo
Chord ha e aroloe ho likhopolo tse ling tsa lipalo tse kang Euclidean geometry, trigonometry, esita le calculus. Tšebeliso e 'ngoe ea trigonometry mabapi le chord ke ho baleng likhutlo selikalikoeng le tšebeliso ea eona ho fumana bolelele ba chord kapa sebaka sa karolo e chitja.
Mohlala, haeba re tseba bolelele ba radius (\(R\)) le sekhutlo se bohareng (\(\theta\)) se bopilweng ke di-radii tse pedi, re ka sebedisa diforomo tsa trigonometric ho fumana bolelele ba chord. Ena ke mohlala o tiileng wa kamoo dipalo di ka sebediswang ho rarolla mathata a lefatshe la nnete ka tsela e sebetsang haholo.
Mohlala oa Palo
A re re re na le selikalikoe se nang le radius \( R = 10 \) cm le angle e bohareng \( \theta = 60^\circ \). Re sebelisa foromo ea bolelele ba chord, re ka bala ka tsela e latelang:
\[ c = 2 \cdot R \cdot \sin \left( \dfrac{\theta}{2} \right) \]
\[ c = 2 \cdot 10 \cdot \sin \left( \dfrac{60^\circ}{2} \right) \]
\[ c = 20 \cdot \sin(30^\circ) \]
\[ c = 20 \cdot 0.5 \]
\[ c = 10 \, \mongolo{cm} \]
Kahoo, bolelele ba khoele ea seqha tabeng ena ke 10 cm.
Qetello
Didikadikwe le di-chord ke dikarolo tse pedi tsa bohlokwa tsa jeometri tse nang le ditshebediso tse ngata mafapheng a fapaneng a saense le bophelong ba letsatsi le letsatsi. Ho utlwisisa dibopeho tsa motheo tsa didikadikwe le di-chord ho re fa temohisiso e tebileng mabapi le hore na dintho di sebetsa jwang sebakeng sa mahlakore a mabedi mme hape ho re thusa ho rarolla mathata a fapaneng a sebetsang.
Ka sengoloa sena, re tšepa hore u fumane kutloisiso e betere ea likhopolo tsa li-circles le li-chord, le kamoo li ka sebelisoang kateng maemong a sebele. Ebang u seithuti, setsebi, kapa motho ea nang le thahasello ea lipalo, ho tseba likhopolo tsena ho tla ntlafatsa temohisiso ea hau le tsebo ea hau ea tlhahlobo.
