Question

In which of the following, unique $△$ ABC cannot be constructed with the given information? Assume AB = 5 cm for each of the options.

• A. BC = 4 cm, CA = 3 cm
• B. $\angle A={60}^{\circ }$, $\angle B={30}^{\circ }$
• C. $\angle C={60}^{\circ }$, BC = 3 cm
• D. BC = 7 cm , $\angle B={30}^{\circ }$

Answer 1

The correct option is C $\angle C={60}^{\circ }$, BC = 3 cm

In case of BC = 4cm and CA = 3cm, the measure of all 3 sides is given so it is possible to construct a unique triangle.

When we know the measure of angles A and B and the included side AB, it is possible to construct a unique triangle.

We can also construct a unique triangle if we know the measure of 2 sides AB and BC along with the measure of the included $\angle B$.

However it is not possible to construct a unique triangle when we are given the measure of 2 sides AB and BC but the angle given is $\angle C$ which is not the included angle.