sas: side, angle, side
Given
\(b\), \(\angle C\), \(a\) - two sides and the included angle
Analysis
We can locate the first vertex of the triangle, \(C\), by constructing the given angle \(C\). We can then use this vertex as a center of two circles constructed with the given sides \(b\) and \(c\) as their radii. The intersection of these circles with the sides of the constructed angle \(C\) locates the remaining two vertexes of the triangle, \(A\) and \(B\).
Construction Outline
Construct the given angle \(C\) with the vertex at an arbitrary point \(C\). Construct a \(Cir(C, a)\) and a \(Cir(C, b)\). The intersection of these two circles with the sides of the angle \(C\) locates the remaining two vertexes of the triangle, \(A\) and \(B\)
Sample Construction
$$C, Z$$
$$Ln(C, Z)$$
$$Y \colon \quad \angle YCZ = \angle C$$
$$Ln(C, Y)$$
$$Cir(C, a)$$
$$Cir(C, a) \; \cap \; Ln(C, Z) = B \colon \quad CB = a$$
$$Cir(C, b)$$
$$Cir(C, b) \; \cap \; Ln(C, Y) = A \colon \quad CA = b$$
$$Ln(A, B)$$
$$\triangle ABC$$
\(\blacksquare\)