Determining the Sides of a Triangle, Given are Perimeter and three AnglesI was studying for some exams when a wild question appeared. It looks like this:Given that the perimeter of a triangle is 180 inches. If the angles of the triangles are in the ratio 5:6:7, determine the sides of the triangle.

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Illuddybopylu · Accepted Answer

By law of sines:      a          sin      ⁡              50                  ∘                      =      b          sin      ⁡              60                  ∘                      =      c          sin      ⁡              70                  ∘                    and   a  +  b  +  c  =  180Let       a          sin      ⁡              50                  ∘                      =  kHence,   a  =  k  sin  ⁡      50          ∘      ,   b  =  k  sin  ⁡      60          ∘      ,   c  =  k  sin  ⁡      70          ∘       and  k  sin  ⁡      50          ∘        +  k  sin  ⁡      60          ∘        +  k  sin  ⁡      70          ∘        =  180  ,which gives  k  =      180          sin      ⁡              50                  ∘                    +      sin      ⁡              60                  ∘                    +      sin      ⁡              70                  ∘                    and from here we can now get the values of a, b and c.

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