Izici zobude zikanxantathu ongakwesokudla

Kule ncwadi, sizocabangela izici eziyinhloko zokuphakama kunxantathu olungile, futhi sihlaziye izibonelo zokuxazulula izinkinga kulesi sihloko.

Qaphela: unxantathu ubizwa unxande, uma enye yama-engeli ayo ilungile (ilingana no-90°) kanti amanye amabili ashubile (<90°).

Ukuphakama kwezakhiwo kunxantathu ongakwesokudla

Impahla 1

Unxantathu wesokudla unobude obubili (h₁ и h₂) iqondane nemilenze yayo.

ubude besithathu (h₃) yehlela ku-hypotenuse isuka endaweni engakwesokudla.

Impahla 2

I-orthocenter (iphoyinti le-intersection of heights) likanxantathu ongakwesokudla liku-vertex ye-engeli engakwesokudla.

Impahla 3

Ukuphakama kukanxantathu ongakwesokudla odonseleka ku-hypotenuse kuyayihlukanisa ibe ngonxantathu abangakwesokudla abafanayo, nabo abafana nowasekuqaleni.

1. △ABD ~ △ABC kuma-engeli amabili alinganayo: ∠I-ADB = ∠I-LAC (imigqa eqondile), ∠ABD = ∠I-ABC.

2. △I-ADC ~ △ABC kuma-engeli amabili alinganayo: ∠I-ADC = ∠I-LAC (imigqa eqondile), ∠I-ACD = ∠I-ACB.

3. △ABD ~ △I-ADC kuma-engeli amabili alinganayo: ∠ABD = ∠I-DAC, ∠ABABI = ∠I-ACD.

Ubufakazi: ∠ABABI = 90° – ∠I-ABD (ABC). Ngesikhathi esifanayo ∠I-ACD (ACB) = 90° – ∠ABC.

Ngakho-ke, ∠ABABI = ∠I-ACD.

Kungafakazelwa ngendlela efanayo nokuthi ∠ABD = ∠I-DAC.

Impahla 4

Kunxantathu ongakwesokudla, ubude obudonselwa ku-hypotenuse bubalwa ngale ndlela elandelayo:

1. Ngokusebenzisa izingxenye ze-hypotenuse, eyakhiwe ngenxa yokuhlukaniswa kwayo ngesisekelo sobude:

2. Ngobude bezinhlangothi zikanxantathu:

Le fomula ithathwe ku Izici ze-sine ye-engeli ebukhali kunxantathu ongakwesokudla (i-sine ye-engeli ilingana nesilinganiso somlenze ophambene ne-hypotenuse):

Qaphela: kunxantathu ongakwesokudla, izici zobude ezijwayelekile ezethulwe eshicileleni lethu – nazo ziyasebenza.

Isibonelo senkinga

Umsebenzi 1

I-hypotenuse kanxantathu ongakwesokudla ihlukaniswe ngobude obudonswe kuyo ibe yizigaba ezingu-5 no-13 cm. Thola ubude balokhu kuphakama.

Isixazululo

Masisebenzise ifomula yokuqala ethulwe kuyo Impahla 4:

Umsebenzi 2

Imilenze kanxantathu wesokudla ingama-9 no-12 cm. Thola ubude be-altitude obudonselwa ku-hypotenuse.

Isixazululo

Okokuqala, ake sithole ubude be-hypotenuse eduze (vumela imilenze kanxantathu ibe "kuya" и "B", kanye ne-hypotenuse "vs"):

c² =A² + b² = 9² 12 +² = 225.

Ngenxa yalokho, i- с = 15cm.

Manje singasebenzisa ifomula yesibili kusuka Izakhiwo 4okuxoxwe ngakho ngenhla: