Omonov sherozbek

49-rasm.
S=AB*AD sin =24, 5*6sin =24, sin =4/5 cos =3/5
Kosinuslar teoremasiga ko’ra: BD²=25+36-60cos =61-60*3/5=25
BD=5.
9-misol: Agar rombning tomoni 10 ga, burchaklaridan biri esa 150⁰ga teng bo’lsa, uning yuzi qanchaga teng bo’ladi?
Yechish:

S=absin =10*10sin30⁰=100*1/2=50

30⁰

^.
150<sup>0

50-rasm</sup>
10-misol: To’g’ri to’rtburchakning to’g’ri burchagi uchidan uning diogonaliga tushirilgan perpendikulyar to’g’ri burchakni 3:1 kabi nisbatda bo’ladi. Shu perpendikulyar bilan boshqa diogonali orasidagi burchakni toping.
Yechish. 4x=90⁰, x=22,5⁰, ADB=90-x=67,5⁰.
DBC+ OCB=2 OBC=2*67,5⁰=135⁰.
BOC=180⁰-(135⁰)=45⁰ OAA₁=45⁰.

B C

O

A₁
3x
x
A D
51-rasm.
11-misol: Diogonallari 6 va 8 ga, ular orasidagi burchak 60⁰ ga teng bo’lgan parallelogrammning perimetrini toping.
Y echish:
B y C
x

A D
52-rasm.

AC=8, BD=6, COD=60⁰

12-misol: Trapetsiyaning asoslari 2 va 3 ga, katta asosiga yopishgan burchaklari 30⁰ va 45⁰ ga teng bo’lsa, trapetsiyaning yuzi qanchaga teng bo’ladi?

Yechish: B C

h h
A D

53-rasm.

BC=2, AD=3, A=30⁰, D=45⁰.

13-misol: ABCD to’g’ri to’rtburchakda AD=12, CD=5, O – diogonallarning kesishish nuqtasi. ni toping.

Yechish:
B C

O

5

A 12 D