Question

Given AB = 3 cm, AC = 5 cm and $\angle B={30}^{\circ }$, $\Delta$ABC cannot be uniquely constructed, with AC as base, why?

• A. Two sides and included angle are given.
• B. The other two angles are not given.
• C. The vertex B cannot be uniquely located.
• D. The vertex A coincides with the vertex C.

Answer 1

The correct option is C The vertex B cannot be uniquely located.

The information of two sides and an angle is given, which means we could potentially draw a triangle using SAS criterion. However, SAS criterion requires the measurement of the included angle between the two sides which has a common vertex. But from the information provided, $\angle B$ is given and the sides are $\overline{AB}$ and $\overline{AC}$ which means that $\angle B$ is not the included angle. Hence we cannot construct a unique triangle with AC as the base.