Acute angle △ ABC. Known (b ^ + C ^ - A ^) Tana = √ 3bC 1) find angle a (2) if a = 2, find ∠ a | Math enthusiast | Mathematical art

Acute angle △ ABC. Known (b ^ + C ^ - A ^) Tana = √ 3bC 1) find angle a (2) if a = 2, find ∠ a

The first question is as follows: (b ^ 2 + C ^ 2-A ^ 2) Tana = √ 3bC,
By substituting the cosine theorem B ^ 2 + C ^ 2-A ^ 2 = 2bccosa, 2bcsina = √ 3bC,
That is, Sina = √ 3 / 2 shows that a = 60 degree
The second question of the title, is there a problem? Didn't a find out?

RELATED INFORMATIONS

1. In △ ABC, a, B and C are the opposite sides of angles a, B and C respectively. Given that angle a is an acute angle and B = 3asinb, then Tana=______ ．
2. Given that the three sides of triangle ABC are a, B, C respectively, and the area is s = (a ^ 2 + B ^ 2-C ^ 2) / 4, find Sina + cosa
3. The triangle ABC is known, and its area is s = 1 / 2a2-1 / 2 (B-C) 2, Sina
4. Let ABC be the three sides of △ ABC, and s be the area of triangle. Prove that C ∧ 2-A ∧ 2-B ∧ 2 + 4AB ≥ (4 √ 3) s
5. ABC triangle ABC has three sides, s is the area of triangle, prove C & sup2; - A & sup2; - B & sup2; + 4AB ≥ 4 √ 3S
6. Let a, B, C be the three sides of △ ABC, and s be the area of triangle. Prove that C ^ 2-A ^ 2-B ^ 2 + 4AB ≥ (4 √ 3) s
7. If the inner angles a, B and C of △ ABC are opposite to the sides a, B and C, and if the angles a, B and C form an arithmetic sequence in turn, and (a + C) 2 = 12 + B2, then the area of △ ABC is () A. 6-33B. 63-9C. 23D. 3
8. In △ ABC, a, B and C are the opposite sides of ∠ a, B and C respectively. If a, B and C form an arithmetic sequence, ∠ B = 30 ° and the area of △ ABC is 32, then B is equal to () A. 1+32B. 1+3C. 2+32D. 2+3
9. Given a & 2 + B & 2 + C & 2-ab-3b-2c + 4 = 0, find the value of a + B + C
10. Given a > 0, b > 0, 2C > A + B, prove (1) C ^ 2 > AB (2) C - √ C ^ 2-ab
11. In the triangle ABC, the angle a is equal to 120 degrees, the angle c is equal to 10 degrees, and the angle AB is equal to 12 Make a list of formulas, thank you Be sure to be more detailed In the triangle ABC, the angle a is equal to 120 degrees, the angle c is equal to 10 degrees, and the angle AB is equal to 12 to find BC
12. If A.B.C is trilateral of △ ABC, and A.B satisfies the relation (A-3) &# 178; + [B-4 \ = 0, C is a system of inequalities {X-1 / 3 ＞ x-4, {2x + 3 ＜ 6x + 1 / 2} (Continued) to find the three sides of △ ABC By 22:40 today,
13. The three sides a, B, C of △ ABC satisfy the following conditions: A, B, C = - 178; - 10A + C & # 178; - 26c + 194 + √ (2 / 3b-8) = 0. Try to find the value of a, B, C and judge the shape of △ ABC
14. In △ ABC, the opposite sides of inner angles a, B and C are a, B and C respectively. If C = 60 ° and 3AB = 25-c2, the maximum area of △ ABC is______ ．
15. If the area of △ ABC is s = a # 178; - (B-C) # 178;, then Tan (A / 2)= A1/2 B1/4 C1/8 D1
16. If the three sides of △ ABC are a, B, C, and its area is ᦉ 188; (a ᦉ 178; + B ᦉ 178; - C ᦉ 178;), then what is the internal angle c?
17. It is known that the opposite sides of the internal angles a, B and C of triangle ABC are a, B and C respectively. If a & # 178; + B & # 178; - C & # 178; + AB = 0, then the size of angle c is?
18. Given that the opposite sides of the inner angles a, B and C in the acute angle △ ABC are a, B and C respectively, and a & # 178; + B & # 178; = C & # 178; + AB, find the value of angle C,
19. As shown in the figure, in the triangle ABC, the angle a is equal to 60 degrees It is known that, as shown in the figure, in the triangle ABC, the angles a are equal to 60 degrees CE and BF are bisectors of the triangle ABC angles and intersect at point D Prove that De is equal to DF
20. In ABC, we know that B & # 178; - C & # 178; = A & # 178; + AC, then B =? A. 45 ° B, 120 ° C, 30 ° or 150 ° D, 60 ° or 120 ° C