document.write( "Question 168863: Hi,
\n" ); document.write( "i'm having a bit of trouble do you think you could help?\r
\n" ); document.write( "\n" ); document.write( "the angles of a triangle are in the ratio 3:4:5. If the shortest side has a length of 1 meter, what idsthe length of the longest side?\r
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Algebra.Com's Answer #124637 by jojo14344(1513)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "To begin with, 1st we need to find the ANGLES of the triangle.
\n" ); document.write( "Given Ratio ----> 3:4:5 ------>\"system%28A=45%5Eo%2CB=60%5Eo%2C%2BC=75%5Eo%2C180%5E0%29\"
\n" ); document.write( "Agree? Divide All Angles by 15: \"45%5Eo%2F15=highlight%283%29\";\"60%5E0%2F15=highlight%284%29\";\"75%5Eo%2F15=highlight%285%29\"
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\n" ); document.write( "Let's put those angles in figure so it will be easy to analyze:
\n" ); document.write( " ---> As you see in our drawing,
\n" ); document.write( "\"BC\" is the shortest side = 1meter.
\n" ); document.write( "For argument sake, take a protractor and
\n" ); document.write( "draw on your own to have the right angles and measure the shortest.
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\n" ); document.write( "Here's the trick, determining the longset side because it seems the other 2 sides are so close. Draw a Line from \"B\" to Line \"AC\" and mark point \"D\":
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\n" ); document.write( "We can solve for Line \"BD\" by Pyth Theorem -->\"%28BC%29%5E2=%28BD%5E2%29%2B%28DC%29%5E2\" -->
\n" ); document.write( "\"%28BD%29%5E2=%28BC%29%5E2-%28DC%29%5E2\" ---------> EQN 1
\n" ); document.write( "*note: \"BC=1m\", and we need to find \"DC\"?
\n" ); document.write( "By trigo function: \"Cos75%5Eo=adj%2Fhyp=DC%2FBC\"--->\"DC=%28cos75%5Eo%29%28BC%29=%28cos75%5Eo%29%281%29\" --> \"DC=0.2588m\", Plug in EQN 1:
\n" ); document.write( "\"%28BD%29%5E2=1%5E2-0.2588%5E2=1-0.066977=%280.93302m%29\"
\n" ); document.write( "\"BD=sqrt%280.93302%29=0.966023m\"
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\n" ); document.write( "Now we need to find \"AD\". By Trigo function, \"Tan45%5Eo=BD%2FAD\"
\n" ); document.write( "\"AD=BD%2FTan45%5Eo=0.966023%2FTan45%5Eo=0.966023m\"
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\n" ); document.write( "So, line \"AC=AD%2BDC=0.966023%2B0.2588=1.2248m\"
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\n" ); document.write( "Now,we find Line \"AB\". We can do that either by Trigo Function or Cosine Law. Let's try both and we'll see if the same.
\n" ); document.write( "By Trigo function---> \"Sin45%5Eo=opp%2Fhyp=BD%2FAB\"
\n" ); document.write( "\"AB=BD%2FSin45%5Eo=0.966023%2FSin45%5Eo=1.36616m\"
\n" ); document.write( "Or By Cosine Law ---> \"%28AB%29%5E2=%28AC%29%5E2%2B%28BC%29%5E2-2%28AC%29%28BC%29Cos75%5Eo\"
\n" ); document.write( "\"%28AB%29%5E2=1.2248%5E2%2B1%5E2-2%281.2248%29%281%29Cos75%5Eo\"
\n" ); document.write( "\"%28AB%29%5E2=1.5%2B1-0.6340=1.866\"
\n" ); document.write( "\"AB=sqrt%281.866%29=1.366m\", The same above
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\n" ); document.write( "So here are your measurements:
\n" ); document.write( "\"highlight%28AB=1.366m%29\" ----------> Longest
\n" ); document.write( "\"BC=1m\" -------------------------> Shortest
\n" ); document.write( "\"AC=1.2248m\" --------------------> Middle
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\n" ); document.write( "Thank you,
\n" ); document.write( "Jojo\r
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