document.write( "Question 891836: 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 triangle. I'll try to draw the shape, but I don't know how to describe why the conditions don't determine a unique triangle. I've been stuck on these problems for a week now. They're actually due next week, but I don't want to try it at the last minute. \n" ); document.write( "

Algebra.Com's Answer #540124 by MathTherapy(10552) $\"\"$ $\"About$

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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 triangle. I'll try to draw the shape, but I don't know how to describe why the conditions don't determine a unique triangle. I've been stuck on these problems for a week now. They're actually due next week, but I don't want to try it at the last minute.
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document.write( "Since we’re given 2 sides and a NON-INCLUSIVE angle, we need to use the Law of Sines to determine
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document.write( "how many distinct triangles can be formed. If more than one (1) triangle can be formed from the
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document.write( "given measurements, then the triangle is NOT UNIQUE, or NOT DISTINCT.\r
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document.write( "Since side BC is opposite angle A, then side BC = a = 3
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document.write( "Also, since side AB is opposite angle C, then side AB = c = 5
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document.write( "Using the law of sines, we get: 
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document.write( " ------ Substituting angle A, and sides a & c to determine angle C 
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document.write( " ------ Cross-multiplying
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document.write( "sin C = .833333
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document.write( "Angle C =  =  ≈ 
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document.write( "This means that the 3rd angle, or angle B = , or , or  
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document.write( "    
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document.write( "Now, the reference angle of angle C is in the 2nd quadrant, and is: , or . 
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document.write( "Now, with angle A being , and the reference angle of angle C being , a 2nd triangle, 
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document.write( "with an angle measurement of B = , or B =  CAN BE FORMED.
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document.write( "Therefore, the given triangle with the given measurements represents a NON-DISTINCT or 
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document.write( "NON-UNIQUE triangle, since 2 triangles: one measuring:
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document.write( ", , and , and another measuring:
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document.write( ", , and , can be formed. \n" );
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