document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254711>Question 254711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Special Right Triangles:<BR>\n" );
document.write( "45-45-90 Triangle and the 60-30-90. Can you explain to me how to do it B/c I'm Lost On that part. Can you take it step by step. My teacher cannot teach and I'm in need of help. On this specific part. Send me a few examples. I have a quiz tomorrow so I need this asap. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187060 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=187060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have 2 special triangles; (1) 45-45-90 and (2) 30 - 60-90. These refer to degree measures in a triangle. You may remember that all degrees must add up to 180.<BR>\n" );
document.write( "(1) 45-45-90.<BR>\n" );
document.write( "Notice 2 numbers are the same That means that 2 sides or legs are the same. <BR>\n" );
document.write( "Suppose we call them x and x. We can use Pythagorean theorem to get the hypotenuse as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B+b%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B+b%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where a and be are the legs and a = x and b = x. We get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now x^2 + x^2 are like terms and become 2x^2 as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"2x%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To solve for c, we take a sqrt to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Asqrt%282%29+=+c ALIGN=MIDDLE  ALT=\"x%2Asqrt%282%29+=+c\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the 45- 45- 90 triangle can be expressed as x -x - xsqrt(2).<BR>\n" );
document.write( "We can easily remember this: How many equal angles are there? 2 what kind of a root do I use? 2.It is like we are gluing sqrt(2) onto the side number.<BR>\n" );
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document.write( "EX:<BR>\n" );
document.write( "a = 3, b = 3, c = ?<BR>\n" );
document.write( "using the relationship, we just take the side and glue a sqrt(2) onto it for the hypotenuse. I call this going forward\" because you are going forward from the leg to hypotenuse. Going forward means \"multiply\" So, c = 3sqrt(2)<BR>\n" );
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document.write( "EX:<BR>\n" );
document.write( "a = 18, b = 18, c = ?<BR>\n" );
document.write( "using the relationship, we just take the side and glue a sqrt(2) onto it for the hypotenuse. I call this going forward\" because you are going forward from the leg to hypotenuse. Going forward means \"multiply\" So c = 18sqrt(2).<BR>\n" );
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document.write( "EX: <BR>\n" );
document.write( "a = ?, b = ?, c = 7sqrt(7)<BR>\n" );
document.write( "I call this going backwards. Look at the number in front of the 7sqrt(2), it is 7. The sides a and b are both 7. Going backwards means divide.<BR>\n" );
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document.write( "EX: harder<BR>\n" );
document.write( "a = ?, b = ? , c = 15<BR>\n" );
document.write( "Remember, we are going backward from the hypotenuse to the legs, so we divide by sqrt (2) to get 15/sqrt(2). Don't know if you have sen these yet.<BR>\n" );
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document.write( "(ii) 30-60-90.<BR>\n" );
document.write( "here it is a bit tricky, but here are the rules.<BR>\n" );
document.write( "The side opposite 30 degrees is always 1/2 hypotenuse<BR>\n" );
document.write( "The side opposite 60 degrees is always side opposite 30 number sqrt(3) glued on.<BR>\n" );
document.write( "You can remember this as 30 -> sqrt(3) is needed.<BR>\n" );
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document.write( "EX:<BR>\n" );
document.write( "a = 5, b = 5sqrt(3), c = <BR>\n" );
document.write( "You can use Pythagorean theorem if desired here to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2+%2B+%285sqrt%283%29%29%5E2+=+c%5E2 ALIGN=MIDDLE  ALT=\"5%5E2+%2B+%285sqrt%283%29%29%5E2+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+%2B+75+=+c%5E2 ALIGN=MIDDLE  ALT=\"25+%2B+75+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100+=+c%5E2 ALIGN=MIDDLE  ALT=\"100+=+c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "10 = c.<BR>\n" );
document.write( "Or remember to go forward means double side opposite 30 degree angle to get hypotenuse.<BR>\n" );
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document.write( "EX: <BR>\n" );
document.write( "a = ? b = 8sqrt(3), c = 16<BR>\n" );
document.write( "take 1/2 hypotenuse to get a = 8.<BR>\n" );
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document.write( "EX:<BR>\n" );
document.write( "a = 10, b = ?, c = 20<BR>\n" );
document.write( "take the 10 and glue a sqrt(3) to get 10sqrt(3)\r<BR>\n" );
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document.write( "whew! hope this helps, look through your book and do the odds - they are usually in the back. </SPAN>\n" );
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