In △ ABC, if A2 + B2 = 25, A2-B2 = 7, C = 5, then the height of the largest edge is______ ．

In △ ABC, if A2 + B2 = 25, A2-B2 = 7, C = 5, then the height of the largest edge is______ ．

According to the inverse theorem of Pythagorean theorem, a triangle is a right triangle, C is a hypotenuse, and the height of C is h. according to the area formula s = 12ab = 12CH, ∧ H = 125, we fill in 125

Triangle ABC, a = 5, B = 7, C = 8

120 degrees
Cosine theorem
In a triangle, the big side is opposite to the big angle, so the angle corresponding to B is not big or small
Therefore, CoSb = A & # 178; + C & # 178; - B & # 178; / 2Ac = 1 / 2, i.e., ∠ B = 60 ° and ∠ a + C = 120 °

In △ ABC, a = 8, B = 7, B = 60 °. Find C and s △ ABC

∵ in △ ABC, a = 8, B = 7, B = 60 °, from the cosine theorem: B2 = A2 + c2-2accosb, that is 49 = 64 + c2-8c, the solution: C = 3 or C = 5, then s △ ABC = 12acsin B = 63 or 103

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______ ．

From the known condition A2 + 2B2 + c2-2b (a + C) = 0, it is concluded that, (a-b) 2 + (B-C) 2 = 0  A-B = 0, B-C = 0, that is, a = B, B = C  a = b = C, so the answer is equilateral triangle

Given that the three interior angles a, B and C of angle ABC satisfy 2B = a + C, and the reciprocal of a, B and C on three sides satisfies 2 / b = 1 / A + 1 / C, find the size of angle a, B and C

If 2B = a + C and a + B + C = 180, then B = 60, a + C = 120 （1）
sinA/a=sinB/b=sinC/c
Let Sina / a = SINB / b = sinc / C = t = > 1 / a = t / Sina, 1 / b = t / SINB, 1 / C = t / sinc
By substituting 2 / SINB = 1 / Sina + 1 / sinc （2）
LIANLI (1) (2)
A=B=C=60

If a × 0.8 = B △ 1.8 = C × 1 (a, B, C are all greater than 0), then the order of a, B, C is______ ＞______ ＞______ ．

A × 0.8 = 1A = 1.25b △ 1.8 = 1b = 1.8c × 1 = 1C = 1, so b > a > C

In the triangle ABC, if a ^ 2-B ^ 2 + C ^ 2 + AC = 0, then the angle B is?

According to the cosine theorem, CoSb = (A & # 178; + C & # 178; - B & # 178;) / 2Ac = - AC / 2Ac = - 1 / 2
∵B∈(0,π)∴B=2π/3
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