In △ ABC, three sides a, B and C satisfy a & # 178; + B & # 178; = 25, a & # 178; - B & # 178; = 7, C = 5, and find the height of the longest side

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• 1. In △ ABC, if A2 + B2 = 25, A2-B2 = 7, C = 5, then the height of the largest edge is______ ．
• 2. In △ ABC, if ∠ a - ∠ C = 25 ° and ∠ B - ∠ a = 10 °, then ∠ B=______ ．
• 3. In the triangle ABC, the opposite sides of angles a, B and C are a, B and C respectively. If the square of a + the square of B = 25 and the square of a - the square of B = 7, find the height of the largest side
• 4. In triangle ABC, if a: B: C = 5:7:8, then angle B =?
• 5. It is known that the lengths of three sides of △ ABC are a, B, C respectively, and satisfy a & # 178; + C & # 178; = 2Ab + 2bc-2b & # 178;. It is proved that △ ABC is an equilateral triangle
• 6. Given that a, B and C are the lengths of the three sides of △ ABC and satisfy A2 + 2B2 + c2-2b (a + C) = 0, then the shape of the triangle is______ ．
• 7. Given the trilateral length of △ ABC, a, B, C satisfies a & # 178; = B & # 178; + C & # 178; + BC, find ∠ a
• 8. It is known that the lengths of three sides of the triangle ABC are a, B, C respectively, and a & gt; C, then | C-A | - √ (AC-B) & # 178=
• 9. Given that a, B, C > 0 and 1 / (1 + a) + 1 / (1 + b) + 1 / (1 + C) = 1, we prove that ABC ≥ 8
• 10. If a, B, C > 0. ABC = 8
• 11. In △ ABC, the opposite sides of ∠ a, B and C are a, B and C respectively, and a & # 178; + 2Ab = C & # 178; + 2BC. Try to judge the shape of △ ABC As mentioned above~
• 12. Let a, B, C be the three sides of △ ABC, and (A & # 178; - 2Ab + B & # 178;) + (B & # 178; - 2BC + C & # 178;) = 0, which indicates the shape of △ ABC Urgent,
• 13. If real numbers a, B and C satisfy A2 + B2 + C2 + 4 ≤ AB + 3B + 2c, then 200A + 9b + C=______ ．
• 14. A square + b square + C square - ab-3b-2c + 4 = 0 to find the value of a + B + C, please write the process and briefly explain, thank you
• 15. Given a > 0, b > 0, 2C > A + B, prove (1) C ^ 2 > AB (2) C - √ C ^ 2-ab
• 16. Given a & 2 + B & 2 + C & 2-ab-3b-2c + 4 = 0, find the value of a + B + C
• 17. 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
• 18. 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
• 19. 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
• 20. ABC triangle ABC has three sides, s is the area of triangle, prove C & sup2; - A & sup2; - B & sup2; + 4AB ≥ 4 √ 3S