Question

determine the number of triangles abc possible with the given parts.
b = 154.07° c = 5.8 b = 15.6
how many possible solutions does this triangle have?

Explanation:

Step1: Analyze the given angle

Since \( B = 154.07^{\circ}\) is an obtuse angle (\(B>90^{\circ}\)).

Step2: Apply the rule for obtuse - angled triangle in the ambiguous case (SSA)

In the SSA (side - side - angle) case, when the given angle \(B\) is obtuse, if \(b>c\) (where \(b\) is the side opposite the given angle \(B\) and \(c\) is the other given side), then there is exactly one triangle.

We are given \(b = 15.6\) and \(c=5.8\). Since \(15.6>5.8\) (i.e., \(b > c\))

Answer:

\(1\)