Question

How do you determine the number of possible triangles and find the measure of the three angles given `c=18, b=10, mangleC=120`?

Answer 1

The Ambiguous Case applies only to acute given angles; the given angle is obtuse, therefore, only one triangle exists.
Use The Law of Sines to find `B`
Find A by using `A = 180^@ - C - B`

Explanation:

Here is a reference for the Ambiguous Case

Use The Law of Sines to find B:

`sin(B)/b = sin(C)/c`

`sin(B) = sin(C)b/c`

`B = sin^-1(sin(C)b/c)`

`B = sin^-1(sin(120^@)10/18)`

`B~~ 29^@`

`A = 180 - 120 - 29`

`A ~~ 31^@`