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.

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embizze | High School Teacher | (Level 1) Educator Emeritus

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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:

`9.8^2=3.7^2+5.6^2-2(3.7)(5.6)cosC`

`cosC=-1.2304563668` which is not possible.

Sources:

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