Algebra.Com's Answer #349072 by Edwin McCravy(20060)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
using the law of sines, solve for the missing measures.
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document.write( "A=60 degrees
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document.write( "B=
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document.write( "C=
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document.write( "a=9
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document.write( "b=
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document.write( "c=10
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document.write( "so far i have sin60/9 = sinC/10
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document.write( "This is the AMBIGUOUS case SSA, (side-side-angle) which may have 0 solutions,\r\n" );
document.write( "1 solution, or 2 solutions. If it has 2 solutions we call them triangle ABC\r\n" );
document.write( "with sides a,b,c, and triangle A'B'C' with sides a',b',c'.\r\n" );
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document.write( "I'll tell you in advance that there are two solutions to this problem, \r\n" );
document.write( "The first two figures below show the two solutions, and the third\r\n" );
document.write( "figure below shows them put together with triangle A'B'C' inside of\r\n" );
document.write( "triangle ABC, the blue arc shows that a and a' both equal 9 in length:\r\n" );
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document.write( "   \r\n" );
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document.write( "First solution Second solution (maybe)\r\n" );
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document.write( "A = 60° A' = 60°\r\n" );
document.write( "B = B' = \r\n" );
document.write( "C = C' = \r\n" );
document.write( "a = 9 a' = 9 \r\n" );
document.write( "b = b' = \r\n" );
document.write( "c = 10 c' = 10\r\n" );
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document.write( "We start with what you had:\r\n" );
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document.write( " =  \r\n" );
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document.write( " =  \r\n" );
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document.write( "9·sin(C) = 10·sin(60°)\r\n" );
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document.write( "sin(C) =  \r\n" );
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document.write( "sin(C) = .9622504486 <--- If this had been greater than 1, there\r\n" );
document.write( " whould have been no solution. If this had \r\n" );
document.write( " been exactly 1, there would have been 1 right\r\n" );
document.write( " triangle angle solution. But since it is less \\r\n" );
document.write( " than 1, we can tell that there is either 1 or 2\r\n" );
document.write( " solutions. \r\n" );
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document.write( "If you use your calculator with the inverse sine,\r\n" );
document.write( "you get \r\n" );
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document.write( "C = 74.20683095°.\r\n" );
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document.write( "That is a correct value for angle C. However there is another \r\n" );
document.write( "possible angle with that same sine, which is a second quadrant \r\n" );
document.write( "angle, and it is found by subtracting 74.20683095° from 180°.\r\n" );
document.write( "We'll call it C':\r\n" );
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document.write( "C' = 180° - 74.20683095° = 105.793169°\r\n" );
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document.write( "So we put those two values in:\r\n" );
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document.write( "First solution Second solution (maybe)\r\n" );
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document.write( "A = 60° A' = 60°\r\n" );
document.write( "B = B' = \r\n" );
document.write( "C = 74.20683095°. C' = 105.793169°\r\n" );
document.write( "a = 9 a' = 9 \r\n" );
document.write( "b = b' = \r\n" );
document.write( "c = 10 c' = 10 \r\n" );
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document.write( "To find out whether there are 2 solutions or only 1,\r\n" );
document.write( "we calculate the angles B and B', and see if both\r\n" );
document.write( "are possibilities:\r\n" );
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document.write( "We calculate B by using 180°-A-C = 180°-60°-74.20683095° = 45.79316905°\r\n" );
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document.write( "We calculate B' by using 180°-A'-C' = 180°-60°-105.793169° = 14.20683095°\r\n" );
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document.write( "Since B' came out positive, we know that there are two solutions,\r\n" );
document.write( "[If B' had come out negative, there would have been only 1 solution].\r\n" );
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document.write( "First solution Second solution\r\n" );
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document.write( "A = 60° A' = 60°\r\n" );
document.write( "B = 45.79316905° B' = 14.20683095°\r\n" );
document.write( "C = 74.20683095°. C' = 105.793169°\r\n" );
document.write( "a = 9 a' = 9 \r\n" );
document.write( "b = b' = \r\n" );
document.write( "c = 10 c' = 10 \r\n" );
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document.write( "Now we just have to calculate sides b and b'\r\n" );
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document.write( "To calculate side b:\r\n" );
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document.write( "b·sin(60°) = 9·sin(45.79316905°) \r\n" );
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document.write( "b =  \r\n" );
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document.write( "b = 7.449489743\r\n" );
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document.write( "---\r\n" );
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document.write( "To calculate side b':\r\n" );
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document.write( " =  \r\n" );
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document.write( " =  \r\n" );
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document.write( "b'·sin(60°) = 9·sin(45.79316905°) \r\n" );
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document.write( "b' =  \r\n" );
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document.write( "b' = 2.550510257\r\n" );
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document.write( "So we end up with:\r\n" );
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document.write( "First solution Second solution\r\n" );
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document.write( "A = 60° A' = 60°\r\n" );
document.write( "B = 45.79316905° B' = 14.20683095°\r\n" );
document.write( "C = 74.20683095° C' = 105.793169°\r\n" );
document.write( "a = 9 a' = 9 \r\n" );
document.write( "b = 7.449489743 b' = 2.550510257 \r\n" );
document.write( "c = 10 c' = 10\r\n" );
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document.write( "Edwin \n" );
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