Question

a given ab = 3 cm, ac= 5 cm and angel b =30 degree,triangle abc cannot be uniquely constructed , with ac as base ,why
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Answer 1

Step-by-step explanation:

SOLUTION

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

¯¯¯¯¯¯¯¯

A

B

and

¯¯¯¯¯¯¯¯

A

C

which means that

∠

B

is not the included angle. Hence we cannot construct a unique triangle with AC as the base.

Answer 2

Solution:

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 ᾹB and ᾹC which means that ∠B is not the included angle. Hence we cannot construct a unique triangle with AC as the base.

Correct Answer:

• The vertex B cannot be uniquely located.

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