How do you solve the following triangle using the law of cosines?  a=3.7, b=5.6, c=9.8.Does this triangle have no solution?  I obtained a cosine for angle gamma (c side) of less than -1.

Expert Answers
embizze eNotes educator| Certified Educator

You are correct -- there is no solution.

The triangle inequality theorem -- two sides of a triangle sum to more than the third side. Here 3.7+5.6=9.3<9.8 which is not a triangle.

Using the Law of Cosines to find angle C we get:


`cosC=-1.2304563668` which is not possible.