Nzira yekuwana sei chikonzero chekona katatu

Pakati pezviverengero zvakawanda zvakaitwa kuti uverenge zvakasiyana-siyana zvezviyero zvakasiyana-siyana zvejometri, iri kuwana huwandu hwemutsara. Yeuka kuti katatu ine polyhedron ine mawani matatu. Pasi apa uchawana nzira dzakawanda dzekuverenga huwandu hwevatatu vatatu.

Pakutanga, ngationei kuti tingawana sei runyararo rwekakona katatu kakarurama. Kune avo vakakanganwa, katatu-chinonzi inonzi rectangular, ine angle ye 90 degrees. Rutivi rwekatatu, riri kune rumwe rutivi rwekona yakarurama, rinonzi hypotenuse. Mukuwedzera, ndicho chikamu chakareba kupfuura chetatu. Zvichienderana nematano anozivikanwa, urefu hwehuwandu hunoverengwa sezvinotevera:

• Marefu emakumbo anozivikanwa. Kunyatsoziva munyaya iyi kunotorwa kushandiswa kwechirongwa chePythagoras, iyo inoratidzika seyotevera: chikamu chekufungidzira kwakaenzana nemari yemakumbo emakumbo. Kana tikatarisa katatu yakanaka BKF, apo BK naKF vane makumbo, uye FB inofungidzira, saka FB2 = BK2 + KF2. Kubva pane zvataurwa apa zvinotevera kuti pakuverenga urefu hwekufungidzira kunokosha kusimbisa imwe neimwe yemakumbo emakumbo. Zvadaro wedzera nhamba dzezvidimbu dzakatemerwa uye dzinobvisa ruvara rwepakati yemugumisiro.

Chimbofunga muenzaniso: Tsanga katatu ine kona yakarurama inopiwa. Rimwe cathet is 3 cm, imwe yacho 4 cm. Tsvaga chikonzero. Mhinduro yacho ndeyotevera.

FB2 = BK2 + KF2 = (3cm) 2+ (4cm) 2 = 9cm2 + 16cm2 = 25cm2. Bvisa ruvara rwemukati uye uwane FB = 5cm.

• Inozivikanwa ndiyo cathette (BK) uye yakananga pedyo nayo, iyo inoumbwa nehuwandu uye gumbo iri. Nzira yekuwana sei chikonzero chekatatu? Isu tinoreva iyo inozivikanwa engangani α. Maererano nenzvimbo yekona katatu, iyo inotaura kuti chiyero chehurefu hwemakumbo kusvika pakureba kwekufungidzira kwakaenzana ne cosine yekona pakati pemakumbo aya uye nehuwandu. Tichifunga nezvekwangwani, izvi zvinogona kunyorwa se: FB = BK * cos (α).
• Zinozivikanwa ndiyo cathet (KF) uye yakafanana ngero a, asi ikozvino ichave yakatarisana. Nzira yekuwana sei chirwere munyaya ino? Isu tinoshandura zvose kune zvimwechetezvo zvekona katatu uye tione kuti chiyero chehurefu hwemakumbo kusvikira kureba kwechikonzero chinokwana sine yekona yakatarisana negumbo. Ndiko, FB = KF * chivi (α).

Chimbofunga muenzaniso. Izvo rimwe rectangular triangle BKF ne hypotenuse FB inopiwa. Ngatitii iyo angle F ndiyo 30 degrees, yechipiri b-B inofananidzwa nemadhora makumi matanhatu. Izvo zvinozivikanwa ndeye BK cathet, iyo yakareba masendimita 8. Unogona kuverenga kukosha kwaidiwa sezvinotevera:

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

• Nharaunda yedenderedzwa (R) inotsanangurwa pedyo nekona katatu yakarurama inozivikanwa. Nzira yekuwana sei pfungwa mukufunga nezvechinetso chakadaro? Kubva kune imwe nzvimbo yedenderedzwa yakatsanangurwa nechetatu nekona yakarurama iyo inozivikanwa kuti pakati penhemberedzwa yakadaro inopindirana nechinangwa chekufungidzira kunoparadzanisa hafu. Mumashoko akajeka, radius inoenderana nehafu yenguva. Nokudaro chikonzero chacho chinokwana maviri radii. FB = 2 * R. Kana dambudziko rakafanana rakapiwa munharaunda iyo inenge isingazivikanwi, asi iyo inofanirwa, mumwe anofanira kutarisa kune imwe nzvimbo yedenderedzwa yakatenderera kumativi mana katatu nekona yakarurama, iyo inoti radius yakaenzana nemutauro wakatarwa kunotarisa. Kushandisa zvinhu zvose izvi, dambudziko racho rinogadziriswa nenzira imwecheteyo.

Kana pane mubvunzo, kuti ungawana sei pfungwa ye isosceles yakanyatsotenderera-katatu, ipapo zvose zvinofanira kushandurwa kune imwecheteyo yePythagoras. Asi, kutanga kwezvose, ngatirangarirei kuti isosceles katatu chinokanganisa ine katatu ine mativi maviri akafanana. Munyaya yekona katatu, mitsipa imwechete makumbo. Tine FB2 = BK2 + KF2, asi kubva BK = KF tine zvinotevera: FB2 = 2 BK2, FB = BK√2

Sezvaunogona kuona, kuziva chimiro chePythagorean uye zvinhu zvekona katatu, zviri nyore kwazvo kugadzirisa zvinetso izvo zvakakosha kuverenga urefu hwehutano. Kana zvinhu zvose zvakaoma kukuyeuka, dzidza maitiro akagadzirira kuburikidza nekuisa munzvimbo iyo maziviro anozivikanwa anogona kuverengwa urefu hunoda huwandu hwehuwandu.