Question

Given AB = 3 cm, AC = 5 cm and ∠B=30∘, ΔABC cannot be uniquely constructed, with AC as base, why?

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

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, ∠B is given and the sides are ¯¯¯¯¯¯¯¯AB and ¯¯¯¯¯¯¯¯AC which means that ∠B is not the included angle. Hence we cannot construct a unique triangle with AC as the base.

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