SOLUTION: Provided AB has length 5 cm, BC has length 3 cm, and the measurement of angle A is 30 degrees, draw triangle ABC, and describe why these conditions do not determine a unique triang

Since we’re given 2 sides and a NON-INCLUSIVE angle, we need to use the Law of Sines to determine

how many distinct triangles can be formed. If more than one (1) triangle can be formed from the

given measurements, then the triangle is NOT UNIQUE, or NOT DISTINCT.



Since side BC is opposite angle A, then side BC = a = 3

Also, since side AB is opposite angle C, then side AB = c = 5

Using the law of sines, we get: 

 ------ Substituting angle A, and sides a & c to determine angle C 

 ------ Cross-multiplying



sin C = .833333

Angle C =  =  ≈ 

This means that the 3rd angle, or angle B = , or , or  

    

Now, the reference angle of angle C is in the 2nd quadrant, and is: , or . 

Now, with angle A being , and the reference angle of angle C being , a 2nd triangle, 

with an angle measurement of B = , or B =  CAN BE FORMED.

 

Therefore, the given triangle with the given measurements represents a NON-DISTINCT or 

NON-UNIQUE triangle, since 2 triangles: one measuring:

, , and , and another measuring:

, , and , can be formed.