Bophahamo ba kgutlotharo e nepahetseng

Khatisong ena, re tla nahana ka thepa e ka sehloohong ea bophahamo ka khutlo-tharo e nepahetseng, hape re hlahlobe mehlala ea ho rarolla mathata tabeng ena.

Hlokomela: khutlotharo e bitsoa sekhutlo, haeba e 'ngoe ea li-angles tsa eona e nepahetse (e lekana le 90 °)' me tse ling tse peli li le bohale (<90 °).

Thepa ea bophahamo ka khutlotharo e nepahetseng

Thepa 1

khutlotharo e nepahetseng e na le bophahamo ba bobeli (h₁ и h₂) e tsamaellana le maoto a yona.

bophahamo ba boraro (h₃) e theohela ho hypotenuse ho tloha lehlakoreng le letona.

Thepa 2

The orthocenter (ntlha ea mateano a bophahamo) ea kgutlotharo e nepahetseng e ka vertex ya kgutlo e nepahetseng.

Thepa 3

Bophahamo ba khutlotharo e nepahetseng e huleloang ho hypotenuse e e arola ka likhutlotharo tse peli tse tšoanang tse nepahetseng, tse tšoanang le tsa pele.

1. △US ~ △ABC ka likhutlo tse peli tse lekanang: ∠ADB = ∠LAC (mela e otlolohileng), ∠US = ∠ABC.

2. △ADC ~ △ABC ka likhutlo tse peli tse lekanang: ∠ADC = ∠LAC (mela e otlolohileng), ∠CDA = ∠ACB.

3. △US ~ △ADC ka likhutlo tse peli tse lekanang: ∠US = ∠DAC, ∠BAD = ∠CDA.

Bopaki: ∠BAD = 90° – ∠ABD (ABC). Ka nako e ts'oanang ∠ACD (ACB) = 90° – ∠ABC.

Ka hona, ∠BAD = ∠CDA.

E ka netefatsoa ka mokhoa o ts'oanang hore ∠US = ∠DAC.

Thepa 4

Ka khutlotharo e nepahetseng, bolelele bo huleloang ho hypotenuse bo baloa ka tsela e latelang:

1. Ka likarolo tsa hypotenuse, e entsoeng ka lebaka la ho arohana ha eona ka motheo oa bophahamo:

2. Ka bolelele ba mahlakore a kgutlotharo:

Foromo ena e nkiloe ho Properties of sine of an acute angle ka khutlotharo e nepahetseng (sine ea angle e lekana le karo-karolelano ea leoto le fapaneng le hypotenuse):

Hlokomela: ho kgutlotharo e nepahetseng, bophahamo bo akaretsang bo hlahisitsweng kgatisong ya rona – le tsona di a sebetsa.

Mohlala oa bothata

Mosebetsi 1

Hypotenuse ea khutlotharo e nepahetseng e arotsoe ke bophahamo bo huleloang ho eona ka likarolo tsa 5 le 13 cm. Fumana bolelele ba bophahamo bona.

tharollo

Ha re sebeliseng foromo ea pele e hlahisitsoeng ho Thepa 4:

Mosebetsi 2

Maoto a kgutlotharo e nepahetseng ke 9 le 12 cm. Fumana bolelele ba bophahamo bo huleloang ho hypotenuse.

tharollo

Taba ea pele, a re fumaneng bolelele ba hypotenuse hammoho (tlohela maoto a kgutlotharo “ho” и "B", le hypotenuse ke “vs”):

c² =A² +b² = 9² + 12² = 225.

Ka hona, с = 15cm.

Joale re ka sebelisa foromo ea bobeli ho tloha Thepa 4e tšohliloeng ka holimo: