document.write( "Question 1198385: Three numbers A, B, C are in ratio a: b: c, if the following proportion is true:
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Algebra.Com's Answer #831959 by ikleyn(52799) $\"\"$ $\"About$

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\n" ); document.write( "Three numbers A, B, C are in ratio a: b: c, if the following proportion is true:
\n" ); document.write( "A/a=B/b=C/c. If the angles of a triangle are in ratio 3: 4: 5,
\n" ); document.write( "find the ratio of the corresponding sides
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document.write( "If the angles of the triangle are in ratio A:B:C = 3:4:5, it means that\r\n" );
document.write( "A = 3x, B = 4x, C = 5x,  where x is the common measure.\r\n" );
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document.write( "Then 3x + 4x + 5x = = 180°,  or  12x = 180°,  which implies  x = 180°/12 = 15°.\r\n" );
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document.write( "Hence, A = 45°,  B = 60°,  C = 75°.\r\n" );
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document.write( "Due to the sine law, it implies\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "Thus the ratio of the corresponding sides is  \r\n" );
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document.write( "    a:b:c = sin(45°) : sin(60°) : sin(75°) =  :  :  = \r\n" );
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document.write( "                                           =  :  :  = 1.414 : 1.732 : 1.932 (rounded).   ANSWER\r\n" );
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