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

1 Answer
Douglas K.
Jan 16, 2017

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^@

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