document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177536>Question 177536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. A triangle has two unknown angles  A and  B. If  A is three times the size of  B, and  C  = 39° 40’ 32” , find the magnitudes of  A and  B.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132546 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=132546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> C = 39 degrees 40 minutes 32 seconds<BR>\n" );
document.write( "32 seconds = 32/60 minutes = 32/60/60 degrees<BR>\n" );
document.write( "40 minutes = 40/60 degrees<BR>\n" );
document.write( "add those two together to get:<BR>\n" );
document.write( "39.675555555..... degrees.<BR>\n" );
document.write( "sum of angles of a triangle is 180.<BR>\n" );
document.write( "180 - C = A + B = 180 - 39.6755555.... = 140.3244444...... degrees<BR>\n" );
document.write( "A is 3 * B, so A + B is the same as B + 3*B = 4*B = 140.3244444..... degrees<BR>\n" );
document.write( "this means that B = 140.324444...../4 = 35.0811111..... degrees<BR>\n" );
document.write( "this means that A = 3*B = 105.2433333..... degrees<BR>\n" );
document.write( "---<BR>\n" );
document.write( "if we round to the nearest thousandth of a degree, we get:<BR>\n" );
document.write( "C = 39.676 degrees<BR>\n" );
document.write( "A = 105.243 degrees<BR>\n" );
document.write( "B = 35.081 degrees<BR>\n" );
document.write( "sum of 39.676 + 105.243 + 35.081 = 180 degrees.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "A is 3 * B means that 3* 35.081 = 105.243 means that 105.243 = 105.243 means that this statement (A = 3*B) is true.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the magnitudes are in decimals.<BR>\n" );
document.write( "to convert back to degrees, minutes, and seconds, you need to convert the decimal portion to minutes and seconds.<BR>\n" );
document.write( "do this as follows:<BR>\n" );
document.write( "take the fractional part and multiply by 3600.<BR>\n" );
document.write( "this gets you seconds.<BR>\n" );
document.write( "divide those seconds by 60 to get minutes.<BR>\n" );
document.write( "that would be the integer part of the division.<BR>\n" );
document.write( "take the fractional part of the minutes and multiply by 60 to get the remaining seconds.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to do this, use the unrounded answer, not the rounded answer, since the rounding will introduce some error in the result.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "C = 39.676 degrees<BR>\n" );
document.write( ".676 * 3600 = 2433.6 seconds<BR>\n" );
document.write( "2433.6 / 60 = 40.56 minutes<BR>\n" );
document.write( "number of minutes is 40<BR>\n" );
document.write( "number of seconds is .56 * 60 = 33.6 = 34 seconds<BR>\n" );
document.write( "we know that the number of seconds is 32 because that was given.<BR>\n" );
document.write( "the rounding introduced the error.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "go back and do it again with the unrounded value this time.<BR>\n" );
document.write( "C = 39.675555555.... degrees<BR>\n" );
document.write( "use .675555555.... * 3600 to get seconds (maximum digits the calculator has should do).<BR>\n" );
document.write( "you get 2431.99999999.... seconds<BR>\n" );
document.write( "divide that by 60 to get:<BR>\n" );
document.write( "40.5333333...... minutes<BR>\n" );
document.write( "multiply .5333333..... * 60 to get:<BR>\n" );
document.write( "31.999999998 seconds<BR>\n" );
document.write( "your answer is:<BR>\n" );
document.write( "C = 39 degrees 40 minutes 32 seconds which agrees with the original value provided.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "do the same for A and B.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "A = 105.2433333..... degrees<BR>\n" );
document.write( ".2433333.... * 3600 = 875.99999999.... seconds<BR>\n" );
document.write( ".875.9999999.... / 60 = 14.6 minutes<BR>\n" );
document.write( ".6 * 60 = 36 seconds<BR>\n" );
document.write( "A = 105 degrees 14 minutes 36 seconds<BR>\n" );
document.write( "---<BR>\n" );
document.write( "B = 35.0811111..... degrees<BR>\n" );
document.write( ".0811111.... * 3600 = 292 seconds<BR>\n" );
document.write( "292 / 60 = 4.866666666.... minutes<BR>\n" );
document.write( ".866666666... * 60 = 52 seconds<BR>\n" );
document.write( "B = 35 degrees 4 minutes 52 seconds<BR>\n" );
document.write( "---<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "A = 105 degrees 14 minutes 36 seconds<BR>\n" );
document.write( "B = 35 degrees 4 minutes 52 seconds<BR>\n" );
document.write( "C = 39 degrees 40 minutes 32 seconds<BR>\n" );
document.write( "----<BR>\n" );
document.write( "add these together to get:<BR>\n" );
document.write( "179 degrees 58 minutes 120 seconds<BR>\n" );
document.write( "this adds up to 180 degrees so the conversion from decimals to minutes and seconds is good.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "your answer is:<BR>\n" );
document.write( "A = 105 degrees 14 minutes 36 seconds<BR>\n" );
document.write( "B = 35 degrees 4 minutes 52 seconds<BR>\n" );
document.write( "---\r<BR>\n" );
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document.write( " </SPAN>\n" );
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