Imibuzo Yesibonelo kanye Nengxoxo Yemibuthano Nama-Chords
Indilinga ingenye yezimo eziyisisekelo zejiyometri ezivame ukufundwa ezibalweni. Umqondo owodwa obalulekile ohlobene nezindilinga yi-chord, okuwumugqa oxhumanisa amaphuzu amabili endilinga ngaphandle kokudlula phakathi nendawo. Ukuqonda izindilinga nama-chord kubalulekile ekutadisheni i-geometry. Lesi sihloko sizoxoxa ngezibonelo eziningana zezinkinga kanye nezingxoxo ezihlobene nezindilinga nama-chord ukuze sijulise ukuqonda kwethu le mibono.
Ukuqonda Okuyisisekelo
Umbuthano
Indilinga iyiqoqo lawo wonke amaphuzu endaweni eqondile aqhelelene kakhulu nephuzu elinikeziwe elibizwa ngokuthi isikhungo. Uma isikhungo sendilinga singu-O kanti irediyasi yendilinga ingu-r, khona-ke indilinga ingavezwa nge-equation (x – O_x)² + (y – O_y)² = r² ngesimo seCartesian.
Intambo yokukhothama
I-chord embuthanweni umugqa oxhumanisa amaphuzu amabili embuthanweni. Ubude be-chord abuxhomekile kuphela erediyasini yembuthano kodwa futhi nasesayizini we-engeli ephakathi ebheke kuyo.
Imibuzo Eyisibonelo Nengxoxo
Umbuzo 1:
Umbuzo: Unikezwe indilinga enobubanzi obuyi-10 cm kanye ne-chord AB enobude obuyi-16 cm. Thola ibanga elifushane kakhulu ukusuka enkabeni yendilinga kuya ku-chord.
Ingxoxo:
Ukuze sithole ibanga elisuka enkabeni yendilinga liye ku-chord, singasebenzisa ifomula kanxantathu efanele eyakhiwe phakathi kwe-radius, ibanga elisuka enkabeni liye ku-chord, kanye nengxenye yobude be-chord.
Ake sithi iphuzu u-O liyisikhungo sendilinga kanti iphuzu u-P liyisici esiphakathi kwe-chord u-AB eqondene no-AB. Ngakho-ke, i-OP ibanga elisuka enkabeni yendilinga u-O liye kwi-chord u-AB.
Kunxantathu i-OAP (unxantathu wesokudla ku-P), singasebenzisa i-Pythagorean Theorem:
OP² + AP² = OA²
Siyazi ukuthi:
– OA (irediyasi yendilinga) = 10 cm
– AB (ubude bentambo yomnsalo) = 16 cm, ngakho-ke AP = 16/2 = 8 cm.
Faka amanani aziwayo ku-equation:
I-OP² + 8² = 10²
I-OP² + 64 = 100
I-OP² = 100 – 64
I-OP² = 36
OP = √36
I-OP = 6
Ngakho-ke, ibanga elifushane kakhulu ukusuka enkabeni yendilinga kuya ku-chord liyi-6 cm.
Umbuzo 2:
Umbuzo: Indilinga ene-O ephakathi inobubanzi obungu-8 cm. I-chord AB yakha i-engeli ephakathi ∠AOB engu-120°. Nquma ubude be-chord AB.
Ingxoxo:
Ukuze sibale ubude be-chord eyakha i-engeli ephakathi (θ), singasebenzisa ifomula:
AB = 2 × r × isono(θ/2)
Di mana:
– r yirediyasi yendilinga (8 cm kulo mbuzo)
– θ yi-engeli eyenziwe yi-chord enkabeni yendilinga (120° kule nkinga)
Faka amanani aziwayo esikhundleni sawo:
AB = 2 × 8 cm × isono(120°/2)
AB = 16 cm × sin(60°)
AB = 16 cm × (√3 / 2)
AB = 8√3 cm
Ngakho-ke, ubude be-chord AB bungu-8√3 cm.
Umbuzo 3:
Umbuzo: Indilinga enobubanzi obungu-13 cm kanye ne-chord AB ingama-5 cm ukusuka enkabeni yendilinga. Thola ubude be-chord AB.
Ingxoxo:
Kulesi simo, singasebenzisa unxantathu ofanele owakhiwe ukuthola ubude be-chord. Ake iphuzu u-O libe yisikhungo sendilinga, iphuzu u-P libe yiphuzu ku-chord eseduze nendawo ephakathi, bese u-AB abe yi-chord.
Siyazi:
– OA (irediyasi yendilinga) = 13 cm
– OP (ibanga eliphakathi nendawo kuya kumnsalo) = 5 cm.
Kunxantathu we-OAP:
OP² + AP² = OA²
Sithola i-AP (isigamu sobude be-chord):
5² + AP² = 13²
25 + AP² = 169
I-AP² = 169 – 25
I-AP² = 144
I-AP = √144
I-AP = 12
Ngakho-ke, ubude be-chord AB = 2 × AP = 2 × 12 = 24 cm.
Umbuzo 4:
Umbuzo: Uma unikezwe indilinga enobubanzi obuyi-10 cm. I-chord AB inobude obuyi-12 cm. Thola usayizi we-engeli ephakathi ∠AOB.
Ingxoxo:
Kulesi simo, sidinga ukusebenzisa okuphambene nomsebenzi we-trigonometric ukuze sinqume i-engeli ephakathi ∠AOB. Ngokusekelwe kufomula yobude be-chord ehlanganisa i-engeli ephakathi θ, singayibhala kabusha ifomula ukuze sibale θ:
AB = 2 × r × isono(θ/2)
Kuphi:
– r yirediyasi yendilinga (10 cm)
– I-AB ubude bentambo yomnsalo (12 cm)
Setha i-equation ukuze uhlukanise i-sin(θ/2):
12 = 2 × 10 × isono(θ/2)
12 = 20 × isono(θ/2)
isono(θ/2) = 12/20
isono(θ/2) = 0.6
Thola inani lika-θ/2:
θ/2 = isono^(-1)(0.6)
θ/2 = 36.87°
Ngakho-ke,:
θ = 2 × 36.87° = 73.74°
Ngakho-ke, i-engeli ephakathi ∠AOB ingu-73.74°.
Isiphetho
Ukufunda imibuthano nama-chord kudinga ukuqonda i-geometry eyisisekelo kanye ne-trigonometry. Ezibonelweni ezingenhla, sibone indlela yokusebenzisa amafomula nama-theorem ahlukahlukene, njenge-Pythagorean Theorem, imisebenzi ye-trigonometric, kanye nezakhiwo eziyisisekelo zemibuthano, ukuxazulula izinkinga.
Ngalezi zinkinga zokuzijwayeza, kunethemba lokuthi ukuqonda okujulile kobudlelwano phakathi kwe-radius, ubude be-chord, kanye ne-engeli ephakathi ephumela kungafinyelelwa. Ukuqonda lo mqondo akusizi nje kuphela ezibalweni zesikole kodwa futhi nasekusetshenzisweni kwansuku zonke emikhakheni ehlukahlukene yesayensi nobunjiniyela.
