2-dars 3 Burchaklar
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2-DARS
- Bu sahifa navigatsiya:
- 3.3.3. To`g`ri burchakli uchburchak 1.
- Katetlarning gipotenuzadagi proyeksiyalari 1.
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3.3.2 . Burchaklar 3.3.3. To’g’ri burchakli uchburchak Katetlarning gipotenuzadagi proyeksiyalari 3.3.2. Burchaklar 1. (96-3-55) Uchburchak ikkita burchagi yig`indisining kosinusi 1/3 ga teng. Uchinchi burchagining kosinusini toping. A)
B)
C)
D)
E)
burchagi ga, C uchdagi ichki burchak ga teng, B uchdagi tashqi burchakni toping. A)
B) C) D) E) 3. (96-7-36) Uchburchakning ikkita burchagi qiymatlarining nisbati 1:2 kabi. Uchinchi burchagi shu burchaklarining kichigidan ga katta. Uchburchakning katta burchagini toping. A)
B) C) D) E) 4. (96-11-57) Uchburchakni ikkita burchagi yig`indisining kosinusi ¼ ga teng. Uchinchi burchagining kosinusini toping. A)
B)
C)
D)
E)
5. (96-12-35) Uchburchak ikkita burchagi yig`indisining kosinusi 1/2 ga teng. Uchinchi burchagining kosinusini toping. A)
B)
C)
D)
E)
qiymatlari nisbati 3:4 kabi, uchinchisiniki esa shu burchaklarning kattasidan ga katta. Uchburchakning katta burchagini toping. A) B) C) D) E) 7. (97-4-46) Uchburchak ikki burchagi yig`indisining sinusi 1/3 bo`lsa, uchinchi burchagining sinusi qanchaga teng bo`ladi? A)
B)
C)
D)
E)
8. (97-5-43) Agar uchburchakning A,B va C burchaklari 1;2 va 3 sonlarga proporsional bo`lsa, B burchakni toping. A)
B) C) D) E) 9. (97-7-36) Uchburchak ikkita burchagining qiymatlari nisbati 5:9 kabi, uchinchi burchagi shu burchaklarning kichigidan ga kichik. Uchburchakning eng kichik burchagini toping. A)
B) C) D) E) 10. (97-9-43) Agar uchburchaklarning burchaklari 5,6 va 7 sonlariga proporsional bo`lsa, uchburchakning katta burchagini toping. A)
B) C) D) E) 11. (97-9-106) Uchburchak ikki burchagi yig`indisining kotangensi 1/6 bo`lsa, uchinchi burchagining kotangensini toping. A)
B)
C)
D)
E)
kattaliklari nisbati 3:2 ga teng. Uchinchi burchagi shu burchaklarning kattasidan ga kichik. Uchburchakning kichik burchagini toping. A) B) C) D) E) 13. (98-2-45) Uchburchakning ikkita tashqi burchagi yig`indisi ga teng. Uning shu burchaklariga qo`shni bo`lmagan ichki burchagini toping. A) B) C) D) E) 14. (99-4-38) ABC uchburchak B burchagi to`g`ri burchak: N nuqta esa A va C burchaklar bissektrisalarining kesishish nuqtasi. ANC burchakning qiymatini toping. A) B) C) D) E) 15. (00-2-39) ABC uchburchakda va AB>BC bo`lsa, ning mumkin bo`lgan x qiymatlari qaysi javobda ko`rsatilgan? A)
B) C)
D) E)
16. (00-3-73) Uchburchakning burchagiga qo`shni bo`lmagan ichki burchaklarning nisbati 5:4 kabi. Shu ichki burchaklarining kichigini toping. A)
B) C) D) E) 17. (00-6-34) Uchburchakning ikkita tashqi burchaklari va ga teng. Uning uchinchi tashqi burchagini toping. A)
B) C) D) E) 18. (00-8-62) Agar A,B va Clar uchburchakning burchaklari bo`lsa,
nimaga teng? A)
B)
C) –
D) sin C E) cos C 19. (97-1-28) Teng yonli uchburchakning yon tomonga tushirilgan balandligi bilan ikkinchi yon tomoni orasidagi burchak ga teng. Teng yonli uchburchakning asosidagi burchagini toping. A)
B) C) D) E) 20. (97-2-18) Teng yonli uchburchakning uchidagi tashqi burchagi o`sha uchdagi ichki burchagidan 4 marta katta. Uchburchakning asosidagi tashqi burchagi necha gradus? A) 100 B) 102 C) 96 D) 108 E) 104
burchagi . Asosidagi burchaklarning bissektrisalari kesishishidan hosil bo`lgan o`tkir burchakni toping. A)
B) C) D) E) aniqlab bo`lmaydi 22. (97-8-18) Teng yonli uchburchakning uchidagi burchagi ga teng. Yon tomoniga o`tkazilgan balandlik va asosi orasidagi burchakni toping. A) B) C) D) E) 23. (98-11-81) Teng yonli uchburchakning asosidagi burchagi ga teng. Bu uchburchakning yon tomonlari orasidagi burchakka qo`shni bo`lgan tashqi burchagining qiymatini toping. A)
B) C) D) E) 24. (99-4-37) Teng yonli uchburchakning uchidagi burchagi ga teng. Uning yon tomoniga tushirilgan balandligi bilan asosi orasidagi burchakni toping. A) B) C) D) E) 25. (00-6-36) Teng yonli uchburchakning asosidagi burchagi ga teng. Shu uchburchakning yon tomoni va ikkinchi yon tomoniga tushirilgan balandligi orasidagi burchakni toping. A)
B) C) D) E) 26. (00-6-37) Teng yonli ABC uchburchakda AC-asos, CD-C burchakning bissektrisasi va ga teng bo`lsa, burchak B ning kattaligini toping.. A) B) C) D) E) 27. (00-5-52) Uchburchak o`tkir burchaklari bo`lishi uchun
va burchaklari orasidagi qanday munosabat o`rinli bo`lishi kerak? A) B) C) D) E) 28. (00-5-67) ning qanday eng katta qiymatida istalgan ABC uchburchak uchun
tengsizlik hamisha o`rinli bo`ladi? A) 1 B) 2 C) 3/2 D) 5/2 E) 3 29. (01-2-39) Uchburchakning burchaklari arifmetik progressiyani tashkil etadi. Agar uchburchakning eng kichik burchagi bo`lsa, eng katta burchagini toping. A) B) C) D) E) 30. (01-6-52) Teng yonli uchburchakning asosidagi tashqi burchagi, unga qo`shni burchagidan ga katta. Teng yonli uchburchakning uchidagi burchagini toping. A) B) C) D) E) 31. (01-7-54) Teng yonli uchburchakning ichki burchaklari va undagi tashqi burchagi yig`indisi (21/16) ga teng. Uchburchakning teng burchaklari yig`indisini toping. A)
B)
C)
D)
E)
32. (01-8-36) Uchburchakning tashqi burchaklaridan biri
ga, shu burchakka qo`shni bo`lmagan burchaklarning ayirmasi ga teng. Uchburchakning ichki burchaklari kattasini toping. A) B) C) D) E) 33. (01-8-38) ABC uchburchakning B va C burchaklari bissektrisalari burchak ostida kesishadi. A burchakning qiymatini toping. A) B) C) D) E) 34. (02-4-45) Teng yonli uchburchakning asosidagi burchak uning uchidagi burchakning 75% iga teng. Uchburchakning uchidagi burchagini toping. A)
B) C) D) E) to`g`ri javob keltirilmagan 35. (02-5-48) Teng yonli uchburchakning uchidagi burchagi ga teng. Asosidagi burchakning bissektrissasi va shu burchakka qarama-qarshi tomon orasidagi burchakni toping. A)
B) C) D) E) 36. (02-8-23) ABC uchburchakda A va B burchaklari bissektrisalari kesishishidan hosil bo`lgan kichik burchak ga teng. Uchburchakning C burchagini toping. A)
B) C) D) E) 37. (02-9-48) AN ABC uchburchakning bissektrisasi. Agar AB=AN va bo`lsa, B burchak necha gradusga teng? A) B) C) D) E) 38. (03-2-45) Uchburchakning ikkita burchagi yig`indisi ga teng. Shu burchaklarning bissektrissalari kesishishidan hosil bo`lgan burchaklardan kichigi necha gradusga teng? A)
B) C) D) E) 39. (03-3-56) Teng yonli uchburchakning asosidagi burchagi ga teng. Shu uchburchakning yon tomonidan biri va ikkinchi tomonga tushirilgan balandligi orasidagi burchakni toping. A)
B) C) D) E) 40. (03-3-12) Teng yonli uchburchakning uchidagi tashqi burchagi o`sha uchidagi ichki burchakdan 4 marta katta. Uchburchakning asosidagi tashqi burchagi necha gradus? A) B) C) D) E)
1. (96-10-43) To`g`ri burchakli uchburchak katetlaridan biri 12 sm,gipotenuzasi esa ikkinchi
katetdan 6 sm uzun. Gipotenuzaning uzunligini toping. A) 15 B) 25 C) 26 D) 18 E) 32 2. (96-1-40) To`g`ri burchakli uchburchakning gipotenuzasi 25sm, katetlari esa o`zaro 3;4 nisbatda. Shu uchburchakning kichik katetini toping. A) 10 B) 12 C) 9 D) 15 E) 20 3. (96-9-91) To`g`ri burchakli uchburchak katetlaridan biri 12 sm, ikkinchisi esa gipotenuzasidan 8 sm qisqa. Shu uchburchak gipotenuzasini toping. A) 15 B) 16 C) 25 D) 13 E) 19 4. (97-1-33) Uchburchak burchaklarining kattaliklari nisbati 1;1;2 kabi, katta tomonining uzunligi esa 13 ga teng. Uchburchakning katta tomoniga tushirilgan balandligini toping. A) 6,5 B) 12 C) 8 D) 5 E) 10
gipotenuzasining shu gipotenuzaga tushirilgan medianaga nisbatini toping.. A) 3 B) 4 C) 2,5 D) 2 E) 1,5 6. (00-1-55) Agar m>n>0 bo`lsa,
va c=2mn uchburchak tomonlarining uzunliklari bo`lsa, quyidagi tasdiqlardan qaysi biri to`g`ri? A) uchburchak o`tkir burchakli B) uchburchak o`tmas burchakli C) Uchburchak to`g`ri burchakli D) asosidagi burchaklari ga teng bo`lmagan teng yonli uchburchak E) muntazam uchburchak
kabi bo`lgan uchburchakning katta tomoniga tushirilgan medianasi 12.5 ga teng. Uchburchakning katta tomonini toping.
A) 20 B) 16 C) 25 D) 32 E) 26 8. (00-7-42) ABC uchburchakning C uchidagi tashqi burchagi ga teng. Agar CA=12 va CB=5 bo`lsa, AB tomonga tushirilgan CD mediananing uzunligini toping. A) 6 B) 6,5 C) 5 D) 5,5 E) 7
uchburchakning katta tomoniga o`tkazilgan medianasini toping. A) 7 B) 6 C) 3 D) 4 E) 5 10. (02-4-49) Uchburchak burchaklari 1:2:3 kabi nisbatda. Uchburchak katta tomonining kichik tomoniga nisbatini toping. A) 1 B) 2 C) 3 D) 4 E) 5 11. (02-8-31) ABC to`g`ri burchakli uchburchakda AB gipotenuza, AM va BN bissektrisalar. Agar AB=12 va
bo`lsa, Mnning uzunligini toping. A) 5 B) 2,5 C) D) 6 E) 4 12. (03-11-33) To`g`ri burchakli uchburchakda o`tkir burchaklarining medianalari uzunliklari 15 va ga teng. Gipotenuza uzunligini toping. A) 18 B) 16 C) 20 D) 21 E) 19 13. (05-114-29) To`g`ri burchakli uchburchakning katetlari va
gipotenuzasidagi proyeksiyasini toping. A) 5,4 B)
C) 6 D) 4,8 E)
1. (96-7-45) To`g`ri burchakli uchburchakning katetlari 5:6 kabi nisbatda, gipotenuzasi esa 122 ga teng. Gipotenuzaning balandlik ajratgan kesmalarni toping. A) 45 va 77 B) 42 va 80 C) 50 va 72 D) 32 va 90 E) 60 va 62
kateti 10 sm ga, gipotenuzasi tushirilgan balandligi 6 sm ga teng. Uning ikkinchi katetini toping. A) 9 B) 7 C) 6,5 D) 7,5 E) 8 3. (96-12-94) To`g`ri burchakli uchburchakning bir kateti 5 ga, gipotenuzasi tushirilgan balandlik 3 ga teng. Uning ikkinchi katetini toping. A) 3,5 sm B) 3,75 sm C) 4sm D) 3,8sm E) 3,9sm 4. (97-1-32) To`g`ri burchakli uchburchakning katetlari 15 va 20 ga teng. Katta katetning gipotenuzadagi proyeksiyasini toping. A) 12 B) 14,5 C) 16 D) 16,5 E) 18 5. (97-2-26) To`g`ri burchakli uchburchakning gipotenuzasi 10 ga teng, bir kateti 6 ga teng. Bu katetning gipotenuzasidagi proyeksiyasini toping. A) 4 B) 3,6 C) 4,2 D) 3,4 E) 3,8 6. (97-3-45) Katetlarining nisbati 3:2 kabi bo`lgan to`g`ri burchakli uchburchakning balandligi gipotenuzasini uzunliklaridan biri ikkinchisidan 6 ga ko`p bo`lgan ikki qismga ajratadi. Berilgan uchburchakning kichik kateti proyeksiyasini toping. A) 5,2 B) 4,8 C) 6 D) 8 E) 7,6 7. (97-7-45) Gipotenuzasi 50 ga teng bo`lgan to`g`ri burchakli uchburchakning katetlari nisbati 4;3 ga teng. Gipotenuzaga tushirilgan balandlik uni qanday kesmalarga ajratadi? A) 20 va 30 B) 15 va 35 C) 18 va 32 D) 12 va 38 E) 14 va 36 8. (97-10-45) Katetlarining nisbati 2;3 bo`lgan to`g`ri burchakli uchburchak balandligi gipotenuzasini uzunliklaridan biri ikkinchisidan 2 ga kam bo`lgan
bo`laklarga ajratadi. Gipotenuzaning bo`laklarini toping. A) 2 va 4 B) 5 va 3 C) 0,9 va 3,9 D) 1,6 va 3,6 E) 2,8 va 4,8 9. (97-11-32) To`g`ri burchakli uchburchakning katetlari 24 va 7 ga teng. Kichik katetining gipotenuzadagi proyeksiyasini toping. A)
B) C)
D)
E)
gipotenuzasi 25 ga, katetlaridan biri 10 ga teng. Ikkinchi katetning gipotenuzadan proyeksiyasini toping. A) 14 B) 15,5 C) 18 D) 20,4 E) 21
gipotenuzasi 5 ga, biri katetining gipotenuzadagi proyeksiyasi 1,6 ga teng. Ikkinchi katetining kvadratini toping.
A) 14 B) 16 C) 17 D) 18 E) 15 12. (98-5-34) To`g`ri burchakli uchburchakning gipotenuzasi 6 ga, katetlaridan biri 4 ga teng. Shu katetning gipotenuzasidan proyeksiyasini toping. A) 3 B)
C)
D)
E)
13. (98-6-34) To`g`ri burchakli uchburchakning balandligi gipotenuzani 2 va 18 ga teng bo`lgan kesmalarga ajratadi. Shu balandlikni toping. A) 4 B) 5 C) 12 D) E) 6
gipotenuzasi 13 ga, katetlaridan biri ga teng. Gipotenuza tushirilgan balandlikning uzunligini toping. A) 5 B) 6 C) 7 D) 4 E) 9
9 va 12 ga teng. Kichik katetning gipotenuzadagi proyeksiyasini toping. A) 6 B)
C) 5,4 D) 4,8 E)
gipotenuzasiga tushirilgan balandligi undan 3 va 12 ga teng kesmalar ajraladi. Bu balandlikni toping. A) 5,5 B)
C)
D) 6 E)
gipotenuzasi 13 ga, gipotenuzasiga tushirilgan balandligi 6 ga teng. Katta katetining gipotenuzasiga proyeksiyasini toping. A) 9 B) 4 C) 5 D) 25 E) 7 18. (99-7-34) To`g`ri burchakli uchburchakning gipotenuzasi 8 ga, katetlaridan biri 4 ga teng. Ikkinchi katetining gipotenuzadagi proyeksiyasini toping. A) 4 B) 3 C) 5 D) 7 E) 6 19. (02-3-53) To`g`ri burchakli uchburchak to`g`ri burchak uchidan gipotenuzaga tushirilgan balandlik ham, katetlarining gipotenuzadagi proeksiyalari ayirmasi ham 6 ga teng. Gipotenuzaning uzunligini toping. A)
B) C) D) E) 12 20. (04-101-6) To`g`ri burchakli uchburchakning balandligi gipotenuzani 8 va 18 ga teng qismlarga ajratadi. Shu balandlikni toping. A) 24 B) C) D) 12 E) 8
ga teng bo`lgan to`g`ri burchakli uchburchak gipotenuzasining ikkinchi katetiga nisbati 5:3 ga teng. Uchburchakning yuzini toping. A) 20 B) 48 C) 12 D) 24 E) 15 22. (04-103-6) To`g`ri burchakli uchburchakning balandligi gipotenuzani 3 va 12 ga teng kesmalarga ajratadi. Shu balandlikni toping. A) 12 B) 4 C) 6 D) E)
katetlari 8 va
gipotenuzadagi proyeksiyasini toping. A) 5,4 B)
C) 6 D) 4,8 E)
7 ga, uning gipotenuzaga proyeksiyasi 1,96 ga teng. Ikkinchi katetning uzunligini toping. A) 24 B) 26 C) 12 D) 15 E) 16
gipotenuzasi 25 ga, katetlaridan biri ga teng. Ikkinchi katetning gipotenuzadagi proyeksiyasini toping. A) 18 B) 21 C) 14 D) 20,4 E) 15,5 26. (04-108-6) To`g`ri burchakli uchburchakning balandligi gipotenuzani 98 va 2 ga teng kesmalarga ajratadi. Shu balandlikni toping. A)
B) 14 C) D) E) 28 27. (04-111-6) to`g`ri burchakli uchburchakning balandligi gipotenuzani 32 va 2 ga teng kesmalarga ajratadi. Shu balandlikni toping. A) 16 B) C)
D) E) 8 28. (04-113-6) To`g`ri burchakli uchburchakning balandligi gipotenuzani 5 va 20 ga teng kesmalarga ajratadi. Shu balandlikni toping. A) 10 B) 20 C) D) E)
29. (05-101-20) To`g`ri burchakli uchburchak katetlarining gipotenuzadagi proyeksiyalari 2 va 8 ga teng. Uchburchaklarning yuzini toping. A) 40 B) 16 C) 10 D) 24 E) 20 Download 351.05 Kb. Do'stlaringiz bilan baham: 
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