In the triangle ABC, if C is 60 degrees, then a b c b c a 30

There was a slight mistake in the previous brother's solution steps, such as missing + and bc, cough cough does not affect the answer.

c = 60 degrees.

c^2=a^2+b^2-2abcos60=a^2+b^2-aba/（b+c）+b/（a+c）

a(a+c)+b(b+c)]/[(b+c)(a+c)][a^2+b^2+ac+bc]/[ab+ac+c^2+bc][a^2+b^2+ac+bc]/[ab+ac+bc+(a^2+b^2-ab)]

a^2+b^2+ac+bc]/[a^2+b^2+ac+bc]

In the triangle, by the cosine theorem, cosc=(a 2+b 2-c 2) 2ab so 1 2=(a 2+b 2-c 2) 2ab i.e. ab=a 2+b 2-c 2

c^2=a^2+b^2-ab

a/(b+c)+b/(c+a)=[a(c+a)+b(b+c)]/(b+c)(c+a)

AC+A2+ B2+BC) (BC+AB+C2+AC) is substituted for C2=A2+B2-AB.

a/(b+c)+b/(c+a)=1

According to the cosine theorem, the liquid family.

a^2=b^2+c^2-2bccosa=10c^2/9-c^2/3==7c^2/9

So a troublesome c=under the root number (a 2 c 2) = under the root number (and family 7 9) = root number 7 3

By Cosine Son's virtual mode theorem:

cosc=(a 2+b 2-c 2) 2ab,this slow-reputation"1 2=(9+b 2-49) 2*3*b,—》b 2-3b-40=(b+5)(b-8)=0,—》b=8.

Let a=3x then follow the title, c=5x

Because it is a right-angled triangle, the root limb is divided according to the Pythagorean calendar and has a +b =c so (3x) +16 =(5x).

9x^+216=25x^

x=4c=5x=20

In a triangle, the uppercase abc refers to the angle, and the lowercase abc refers to the side length. And the symbol of the edge of the search state corresponds to the sign of the diagonal. Shoot and miss to do.

According to the cosine theorem, a=7 can be calculated

Because b = 60 degrees, c = 75 degrees.

So a=45°

By the sine theorem, it is known that the jujube is noisy in the early way.

a/sina=c/sinc

asinc=csina

Because sin=sin75°=sin(45°+30°)=sin45°cos30°+sin30°cos45°=(root number 6 + root number 2) 4

Therefore, 8*{(Root number 6 + Root number 2) 4}=c*(Root number 2) 2 Ascension Epoch is c=4 (root number 3) + 4

If you don't understand,