Question

Uchburchakning yuzi 6 ga teng.Shu uchburchakning 3va8 teng tomonlari oarasidagi burchakni toping? ​

Answer 1

Ответ:

S=0.5*a*b*sin@

6=0.5*3*8*sin@

sin@=1/2

@=30°=π/6

Answer 2

Uchburchakning yuzi 6 ga teng. Shu uchburchakning 3 va 8 teng tomonlari orasidagi burchakni topish uchun, trigonometriya formulalaridan foydalanamiz. Uchburchakning tomonlarining uzunliklarini bilmasak ham, burchaklarni topish mumkin.

Uchburchakning tomonlarini a, b va c deb belgilasak, uchburchakning yuzini S formulasi orqali topish mumkin. Uchburchakning yuzi S = sqrt(s(s-a)(s-b)(s-c)), bu yerda s = (a+b+c)/2.

Uchburchakning yuzini bilish uchun, tomonlarini bilishimiz kerak. Bizda uchburchakning yuzi 6 ga teng, shuning uchun s = 6/2 = 3 ga teng bo'ladi.

Uchburchakning tomonlarini topish uchun, burchaklarni topish formulalaridan foydalanamiz. Uchburchakning burchaklarini A, B va C deb belgilasak, trigonometriya formulalari orqali quyidagi tenglamalar hosil qilinadi:

cos(A) = (b^2 + c^2 - a^2) / (2bc) cos(B) = (a^2 + c^2 - b^2) / (2ac) cos(C) = (a^2 + b^2 - c^2) / (2ab)

Bu formulalardan foydalanib, 3 va 8 teng tomonlari orasidagi burchaklarni topishimiz mumkin.

Let's calculate the angles between the sides of the triangle with sides 3 and 8.