document.write( "Question 1207608: Two sides and an angle are given below. Determine whether the given information results in one​ triangle, two​ triangles, or no triangle at all. Solve any resulting​ triangle(s).
\n" ); document.write( "b=8, c=9, B=40degrees\r
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Algebra.Com's Answer #845578 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
given:\r
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\n" ); document.write( "\n" ); document.write( "\"b=8\", \"c=9\", \"B+=40\"degrees\r
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\n" ); document.write( "\n" ); document.write( "using law of sine:\r
\n" ); document.write( "\n" ); document.write( "\"b%2Fsin%28B+%29=c%2Fsin%28C+%29\"\r
\n" ); document.write( "\n" ); document.write( "\"8%2Fsin%2840%29=9%2Fsin%28C%29\"\r
\n" ); document.write( "\n" ); document.write( "\"sin%28C%29=9sin%2840%29%2F8\"\r
\n" ); document.write( "\n" ); document.write( "\"sin%28C%29=0.7231360608973567\"\r
\n" ); document.write( "\n" ); document.write( "\"C=sin%5E-1%280.7231360608973567%29\"\r
\n" ); document.write( "\n" ); document.write( "\"C=0.8083319666202583\"\r
\n" ); document.write( "\n" ); document.write( "\"C=46.314\"
\n" ); document.write( "or
\n" ); document.write( "\"C=+133.69\"°\r
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\n" ); document.write( "\n" ); document.write( "find third angle\r
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\n" ); document.write( "\n" ); document.write( "\"A=180-%2840%2B46.314%29=93.69\"
\n" ); document.write( "or
\n" ); document.write( "\"A=180-%2840%2B133.69%29=6.31\"\r
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\n" ); document.write( "\n" ); document.write( "side \"a=%28b%2Fsin%28B%29%29%2Asin%28A%29\"
\n" ); document.write( "\"a=%288%2Fsin%2840%29%29%2Asin%2893.69%29\"
\n" ); document.write( "\"a=12.42\"\r
\n" ); document.write( "\n" ); document.write( "or
\n" ); document.write( "\"a=%288%2Fsin%2840%29%29%2Asin%286.31%29\"
\n" ); document.write( "\"a=1.37\"\r
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\n" ); document.write( "\n" ); document.write( "Solution 1:\r
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\n" ); document.write( "\n" ); document.write( "Sides:
\n" ); document.write( "\"a+=+12.42\"
\n" ); document.write( "\"b+=+8\"
\n" ); document.write( "\"c+=+9\"\r
\n" ); document.write( "\n" ); document.write( "Angles:
\n" ); document.write( "\"A+=+93.69\" °
\n" ); document.write( "\"B+=+40\" °
\n" ); document.write( "\"C+=+46.314\" °\r
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\n" ); document.write( "\n" ); document.write( "Solution 2:\r
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\n" ); document.write( "\n" ); document.write( "Sides:
\n" ); document.write( "\"a+=+1.37\"
\n" ); document.write( "\"b+=+8\"
\n" ); document.write( "\"c+=+9\"\r
\n" ); document.write( "\n" ); document.write( "Angles:
\n" ); document.write( "\"A+=+6.31\" °
\n" ); document.write( "\"B+=+40\" °
\n" ); document.write( "\"C+=+133.69+\"°\r
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