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

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 $A = {180}^{\circ} - C - B$

#### Explanation:

Here is a reference for the Ambiguous Case

Use The Law of Sines to find B:

$\sin \frac{B}{b} = \sin \frac{C}{c}$

$\sin \left(B\right) = \sin \left(C\right) \frac{b}{c}$

$B = {\sin}^{-} 1 \left(\sin \left(C\right) \frac{b}{c}\right)$

$B = {\sin}^{-} 1 \left(\sin \left({120}^{\circ}\right) \frac{10}{18}\right)$

$B \approx {29}^{\circ}$

$A = 180 - 120 - 29$

$A \approx {31}^{\circ}$