document.write( "Question 88411: Determine the measure of angle B of triangle ACB, given the following information: A=69degrees, a=25feet, b=16feet \n" ); document.write( "
Algebra.Com's Answer #64258 by Edwin McCravy(20055)\"\" \"About 
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Determine the measure of angle B of triangle ACB, given the following information: A=69degrees, a=25feet, b=16feet\r
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document.write( "This is called the \"ambiguous case\", when you \r\n" );
document.write( "are given two sides and an angle which is not \r\n" );
document.write( "included between them.  The ambiguous case has\r\n" );
document.write( "0, 1, or 2 solutions.  \r\n" );
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document.write( "We use the law of sines:\r\n" );
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document.write( "   a          b          c\r\n" );
document.write( "-------- = -------- = --------\r\n" );
document.write( " sin(A)     sin(B)     sin(C)\r\n" );
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document.write( "Here we only need:\r\n" );
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document.write( "   a          b          \r\n" );
document.write( "-------- = -------- \r\n" );
document.write( " sin(A)     sin(B)     \r\n" );
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document.write( "   25          16          \r\n" );
document.write( "--------- = -------- \r\n" );
document.write( " sin(69°)     sin(B)\r\n" );
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document.write( "Cross multiply:\r\n" );
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document.write( "25·sin(B) = 16·sin(69°)\r\n" );
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document.write( "Divide both sides by 25 to solve for sin(B)\r\n" );
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document.write( "             16·sin(69°)          \r\n" );
document.write( "  sin(B) = ------------- \r\n" );
document.write( "                 25 \r\n" );
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document.write( "  sin(B) = .597491473\r\n" );
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document.write( "1. Sometimes this step comes our greater than 1.\r\n" );
document.write( "   If so, there are no solutions. \r\n" );
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document.write( "2. Sometimes this step comes out exactly 1. If so\r\n" );
document.write( "   then B is a right angle and there is 1 solution.\r\n" );
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document.write( "3. Usually this step comes out a positive number\r\n" );
document.write( "   between 0 and 1.  If this is the case, then there\r\n" );
document.write( "   are either one or two solutions.  We must check to \r\n" );
document.write( "   see if there are two solutions.\r\n" );
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document.write( "   (a) Find the first quadrant solution for angle B\r\n" );
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document.write( "         sin(B) = .597491473\r\n" );
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document.write( "       Find the inverse sine of that right side:\r\n" );
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document.write( "              B = 36.6094481°\r\n" );
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document.write( "Since the sine is positive in the 2nd quadrant, there\r\n" );
document.write( "is another solution for B, namely its supplement:\r\n" );
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document.write( "             B = 180 - 36.6094481° = 143.3095519°\r\n" );
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document.write( "Now we calculate what angle C would have to be if that\r\n" );
document.write( "were a possible solution for angle B.\r\n" );
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document.write( "                A + B + C = 180°\r\n" );
document.write( "   69° + 143.3095519° + C = 180°\r\n" );
document.write( "         212.3095519° + C = 180°\r\n" );
document.write( "                        C = 180° - 212.3095519\r\n" );
document.write( "                        C = -32.3095519°\r\n" );
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document.write( "C cannot be a negative angle, so there is but\r\n" );
document.write( "one solution, namely\r\n" );
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document.write( "              B = 36.6094481°\r\n" );
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document.write( "Since the sides are only given to two significant\r\n" );
document.write( "digits, we should round the answer to the nearest \r\n" );
document.write( "degree:\r\n" );
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document.write( "             B = 37°\r\n" );
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document.write( "Edwin
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