How do you determine the number of possible triangles and find the measure of the three angles given #b=12, c=10, mangleB=49#?
Since the given information is for a SSA triangle it is the ambiguous case. In the ambiguous case we first find the height by using the formula
Note that A is the given angle and its side is always a so the other side will be b.
#h < a < b#then then there are two solutions or two triangles.
#h < b < a#then there is one solution or one triangle.
#a < h < b#then there is no solution or no triangle.
#a > b#then there is one solution or one triangle.
#a <=b#there is no solution
Now let's use the Law of Cosine
To find the measure of angle A we use the law of cosine and solve for A. That is,