document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142607>Question 142607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To find the hypotenuse of a right triangle the equation is a2+b2=c2, but what is the equation for finding the hypotenuse of an obtuse triangle.<BR>\n" );
document.write( "Example would be a 12 foot addition to a house with a new roof having an 18 degree angle laid upon an existing roof having a 45 degree angle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103799 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=103799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, there's no hypotenuse to an obtuse triangle. There's the longest side(and I think this the one you're looking for) opposite the greatest angle(>90deg).<BR>\n" );
document.write( "Let's try to picture first your problem so we can solve it better.<BR>\n" );
document.write( "I'll try to explain it clearly in writing.<BR>\n" );
document.write( "The existing foundation has an acute angle of 45deg, name it angle ABC. So it has  a line from A to B and B to C, and the angle is on B which is 45deg, right?<BR>\n" );
document.write( "Now, you added 12 ft to a new roof having  18 deg., and this became a triangle now, right? So we need to close that acute angle to make it a triangle, and that line you added will be from C to A, and we'll assign it \"b\"=12ft. Why \"b\"? Because it's opposite angle B right? Also, you have angle A as 18 deg as it was stated in the problem. Having known that we can compute for angle C:<BR>\n" );
document.write( "By law, all included angles in a triangle equals 180deg.<BR>\n" );
document.write( "A+B+C=180<BR>\n" );
document.write( "18+45+C=180<BR>\n" );
document.write( "C=180-63<BR>\n" );
document.write( "C=117deg (the largest angle)\r<BR>\n" );
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document.write( "Can you pricture the triangle now? I guess so. We have to assign opposite angle A as \"a\" side, and opp. angle C as \"c\" side - and this the one you're looking for.You need 2 laws in trigo to solve this.<BR>\n" );
document.write( "First we need to solve for side \"a\" and we use Sine Law,<BR>\n" );
document.write( "a/sinA = b/sinB<BR>\n" );
document.write( "a/sin18 = 12/sin45<BR>\n" );
document.write( "a= 5.24ft<BR>\n" );
document.write( "Next, we need to use Cosine Law for the side you're looking for, side c (longest side),<BR>\n" );
document.write( "c^2 = a^2 + b^2 - 2abcosC<BR>\n" );
document.write( "=(5.24)^2 + (12)^2 - 2(5.24)(12)cos117<BR>\n" );
document.write( "c=sq rt[171.46 -(- 57.09)]<BR>\n" );
document.write( "c=15.12 ft<BR>\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Jojo\r<BR>\n" );
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