In △ ABC, it is known that a, B and C are the side lengths corresponding to three inner angles a, B and C respectively, and B & # 178; + C & # 178; - A & # 178; = BC (1) Find the size of angle A (2) If B = 1 and the area of △ ABC is 3 √ 3 / 4, find the length of side C

In △ ABC, it is known that a, B and C are the side lengths corresponding to three inner angles a, B and C respectively, and B & # 178; + C & # 178; - A & # 178; = BC (1) Find the size of angle A (2) If B = 1 and the area of △ ABC is 3 √ 3 / 4, find the length of side C

(1) A ^ 2 = B ^ 2 + C ^ 2-2bccosa, so cosa = 1 / 2, a = 60
(2) S = 1 / 2 * bcsina = 1 / 2 * c * sin60 = 1 / 2 * c * radical 3 / 2 = 3 radical 3 / 4
c=3

It is known that: (a + B-C) / C = (B + C-A) / a = (c + a-b) / B, a + B + C ≠ 0. Proof: (a + b) (B + C) (c + a) / ABC = 8

From a / (B-C) + B / (C-A) + C / (a-b) = 0
[a/（b-c）+b/（c-a）+c/（a-b）][（1/(b-c)+1/(c-a)+1/(a-b)]=0
The results show that [A / (B-C) 2 + B / (C-A) 2 + C / (a-b) 2] + (a + b) / [(B-C) (C-A)] + (B + C) / [(C-A) (a-b)] + (c + a) / [(a-b) (B-C)] = 0
Namely [A / (B-C) 2 + B / (C-A) 2 + C / (a-b) 2] + (A2-B2 + b2-c2 + c2-a2) / [(a-b) (B-C) (C-A)] = 0
So a / (B-C) 2 + B / (C-A) 2 + C / (a-b) 2 = 0

In △ ABC, BC = 8, B = 60 ° and C = 75 °, then AC equals ()
A. 42B. 43C. 46D. 323

A = 180 ° - B-C = 45 ° can be obtained from the meaning of the title, and then acsinb = bcsina can be obtained from the sine theorem, that is acsin60 ° = 8sin45 ° and AC = 46 can be obtained from the solution