Solve a triangle given the two angles in which a median split a vertex angleGiven the two angles α 1 and α 2 in which a vertex angle of a triangle is split by the related median m, find the remaining angles of the triangle β and γ.

Question

Solve a triangle given the two angles in which a median split a vertex angleGiven the two angles       α    1   and       α    2   in which a vertex angle of a triangle is split by the related median m, find the remaining angles of the triangle   β and   γ.

ti1k1le2l · Accepted Answer

Step 1By applying the sine law for triangles ABM and AMC, you can get that             s      i      n      α      1              s      i      n      α      2        =            s      i      n      β              s      i      n      γ       holds true.Step 2Since problem statement indicates the given angles   α  1 and   α  2, using triangle&#039;s angles summation property, one would find   γ  =  180  −  α  1  −  α  2  −  β with known ratio             s      i      n      β              s      i      n      (      α      1      +      α      2      +      β      )      . I guess it would be obvious afterwards to evaluate the desired angle   β.

Given the two angles alpha_1 and alpha_2 in which a vertex angle of a triangle is split by the related median m, find the remaining angles of the triangle beta and gamma.

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