document.write( "Question 896330: find the measure of an angle which is 18 degrees 2 minutes 10 seconds less than its complement. \n" ); document.write( "

Algebra.Com's Answer #543416 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
find the measure of an angle which is 18 degrees 2 minutes 10 seconds less than its complement.
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document.write( "The long notation involving degrees, minutes and seconds does make \r\n" );
document.write( "the problem confusing.\r\n" );
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document.write( "So let's first look at and do a similar problem that just uses something\r\n" );
document.write( "simpler, say, 20°.  For instance let's do this problem:\r\n" );
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\n" ); document.write( "find the measure of an angle which is 20° less than its complement.
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document.write( "The equation would come from this.\r\n" );
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document.write( "Then \r\n" );
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document.write( "x = the desired angle\r\n" );
document.write( "90°-x = the complement of x\r\n" );
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document.write( "x = (90°-x)-20°       <-- step 1\r\n" );
document.write( "x = 90°-x-20°         <-- step 2\r\n" );
document.write( "x = 70°-x             <-- step 3 \r\n" );
document.write( "2x = 70°              <-- step 4\r\n" );
document.write( " x = 35°              <-- step 5\r\n" );
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document.write( "So to do our problem we use this as a model to go by.\r\n" );
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document.write( "let's put 18°2'10\" in place of 20° in step 1, and then do step 2:\r\n" );
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document.write( "x = (90°-x)-18°2'10\"  <-- step 1\r\n" );
document.write( "x = 90°-x-18°2'10\"    <-- step 2\r\n" );
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document.write( "To get step 3 we need to subtract 18°2'10\" from 90°:\r\n" );
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document.write( "We start by writing 90° as 89°59'60\".\r\n" );
document.write( "Then we subtract:\r\n" );
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document.write( " 89°59'60\"\r\n" );
document.write( "-18° 2'10\"\r\n" );
document.write( " 71°57'50\"\r\n" );
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document.write( "Now we have something to use in place of the 70° in step 3 of the\r\n" );
document.write( "other problem.\r\n" );
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document.write( "x = 71°57'50\"-x       <-- step 3 \r\n" );
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document.write( "Then step 4 is easy:\r\n" );
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document.write( "2x = 71°57'50\"        <-- step 4\r\n" );
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document.write( "Now to get the last step we have to divide both sides by 2.  That presents a\r\n" );
document.write( "difficulty, because 71 is not divisible by 2, so we have to convert it so that\r\n" );
document.write( "the number of degrees is divisible by 2.  We take 1° away from the 71° to\r\n" );
document.write( "make it something that is divisible by 2, namely 70°, then we change the 1° to\r\n" );
document.write( "60' and add that to the 57' getting 117' and we have:\r\n" );
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document.write( "2x = 70°117'50\"       <-- step 4\r\n" );
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document.write( "But we still have a problem! 117' is not divisible by 2. Now we must convert the\r\n" );
document.write( "minutes so that they are divisible by 2.  So we take 1' away from the 117' to\r\n" );
document.write( "make the number of minutes divisible by 2, namely 116', then we change the 1'\r\n" );
document.write( "that we took away to 60\" and add that to the 50\" getting 110\" and we have:\r\n" );
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document.write( "2x = 70°116'110\"      <-- step 4\r\n" );
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document.write( "Finally step 5 is easy:\r\n" );
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document.write( " x = 35°58'55\"        <-- step 5\r\n" );
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document.write( "Edwin

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