document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112080>Question 112080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This problem includes triangles, but is presented as a pre-calculus problem.  Since I cannot upload the triangle I'll describe it.  Triangle ABC is made up of two triangles.  The smaller triangle is a 45,45,90 and it's height is 7.  The second triangle is larger and is a 30,60,90 it's height is also 7.  I found the hypotenuse and base for the 45,45,90 triangle they are: hypotenuse= 7 square roots of 2 and base= 7.  I am having trouble finding the hypotenuse and base of the 30,60,90 triangle.  How do I solve for this?\r<BR>\n" );
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document.write( "Thank you so very much for your time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81869 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=81869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here are some ratios you can memorize for these two common triangles:<BR>\n" );
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document.write( "In a standard 45-45-90 triangle, the sides are 1, 1, and sqrt(2) where the 1 and the other 1<BR>\n" );
document.write( "are the lengths of the two legs and the sqrt(2) is the length of the hypotenuse. <BR>\n" );
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document.write( "Now that you know this, you can do the problem for the 45-45-90 triangle you were given.<BR>\n" );
document.write( "Note that in the problem you were given the length of one leg was 7 ... and that is 7 <BR>\n" );
document.write( "times the leg in the standard triangle where each leg is 1.  Since one of the legs is 7,<BR>\n" );
document.write( "the other leg must also be 7 (in a 45-45-90 triangle, both legs are the same) and the <BR>\n" );
document.write( "hypotenuse of the given triangle must also be 7 times the hypotenuse of the standard<BR>\n" );
document.write( "45-45-90 triangle ... so it must be 7 times sqrt(2). The answers you got were correct.<BR>\n" );
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document.write( "Now let's go to the standard 30-60-90 triangle. In this standard triangle the hypotenuse<BR>\n" );
document.write( "has a length of 2. The short leg of this triangle (the leg opposite the 30 degree angle)<BR>\n" );
document.write( "has a length of 1, and the long leg of this triangle has a length of sqrt(3).<BR>\n" );
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document.write( "I'm going to assume that the side which is 7 units long is the short leg of the triangle that<BR>\n" );
document.write( "you were given. Therefore, it is 7 times the short leg of the standard triangle. This means<BR>\n" );
document.write( "that every other side of the triangle must be 7 times the corresponding side of the standard<BR>\n" );
document.write( "triangle. Furthermore, this means that the three sides of your given triangle will be:<BR>\n" );
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document.write( "7 times 1 = 7 <=== as discussed above<BR>\n" );
document.write( "7 times sqrt(3) <=== 7 times the longer leg of the standard 30-60-90 triangle<BR>\n" );
document.write( "7 times 2 = 14 <=== 7 times the hypotenuse of the standard 30-60-90 triangle<BR>\n" );
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document.write( "These two triangles (45-45-90 and 30-60-90) are fairly common so you may want to memorize<BR>\n" );
document.write( "what the lengths of each side is in their standard size.  <BR>\n" );
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document.write( "Hope this helps you with your problem.<BR>\n" );
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