Question

given AB=3cm, AC=5cm, angle B=30 degrees angle ABC cannot be uniquely constructed, with AC as the base, why?

a) Three sides are not given.

b) The other two angles are not given.

c) The vertex B cannot be uniquely located.

d) The vertex A coincides with vertex C.

Answer 1

Step-by-step explanation:

Solution

The correct option is D 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

Answer 2

Answer: (a) as the 3 sides are not given ABC cannot be uniquely constructed.

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