document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=579455>Question 579455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm a toymaker. I'm building a toy castle.The watchtower is an octagon. The roof of the tower is made of 8 triangular pieces. The slope of the roof should be 45°. I'm trying to calculate the corners on wich to cut each part of the roof so they fit perfectly. I came up with the following formula but have no way to check it:(((180-(360/Z))/90)*H)/2<BR>\n" );
document.write( "In this formula Z refers to the number of sides and H to the slope of the roof, calculated from a vertical view. English is not my native language, so I hope you can understand wat I want. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371084 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371084\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The way I read your formula, for H=45 and Z=8, we would get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%28180-%28360%2FZ%29%29%2F90%29%2A45%29%2F2=%28%28%28180-%28360%2F8%29%29%2F90%29%2A45%29%2F2=%28%28180-45%29%2F90%29%2A45%2F2=%28135%2F90%29%2A45%2F2=67.5%2F2=33.75 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "but I got a different result.<BR>\n" );
document.write( "This is the way I calculate it for a 45 degree slope. <BR>\n" );
document.write( "View from the top <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-26%2C26%2C-26%2C26%2C%0D%0Ared%28line%28-24.142%2C-10%2C-10%2C-24.142%29%29%2Cred%28line%2810%2C-24.142%2C+24.142%2C-10%29%29%2C%0D%0Ared%28line%28-24.142%2C10%2C-10%2C24.142%29%29%2Cred%28line%2810%2C24.142%2C+24.142%2C10%29%29%2C%0D%0Ared%28line%28-24.142%2C-10%2C-24.142%2C10%29%29%2Cred%28line%2810%2C-24.142%2C-10%2C-24.142%29%29%2C%0D%0Ared%28line%2824.142%2C-10%2C24.142%2C10%29%29%2Cred%28line%28-10%2C24.142%2C10%2C24.142%29%29%2C%0D%0Aline%2810%2C-24.142%2C24.142%2C-24.142%29%2Cline%2824.142%2C-24.142%2C24.142%2C-10%29%2C%0D%0Agreen%28line%280%2C0%2C24.142%2C0%29%29%2C%0D%0Ablue%28line%280%2C0%2C24.142%2C-10%29%29%2Cblue%28line%280%2C0%2C24.142%2C10%29%29%2C%0D%0Alocate%28-0%2C-21%2C2x%29%2Clocate%2814%2C-15%2C2x%29%2Clocate%2816%2C-21%2Cx%2Asqrt%282%29%29%2C%0D%0Alocate%28-24%2C2%2C2x%29%2Clocate%2810%2C3%2Cx%281%2Bsqrt%282%29%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "View from the side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-26%2C26%2C-24%2C28%2C%0D%0Aline%28-24.142%2C0%2C24.142%2C0%29%2Cline%28-24.142%2C0%2C-24.142%2C-26%29%2C%0D%0Aline%2824.142%2C0%2C24.142%2C-26%29%2Cline%28-10%2C0%2C-10%2C-26%29%2Cline%2810%2C0%2C10%2C-26%29%2C%0D%0Aline%28-24.142%2C0%2C0%2C24.142%29%2Cline%280%2C24.142%2C24.142%2C0%29%2C%0D%0Aline%28-10%2C0%2C0%2C24.142%29%2Cline%280%2C24.142%2C10%2C0%29%2C%0D%0Alocate%287.5%2C27%2Cx%281%2Bsqrt%282%29%29%29%2Carrow%287.5%2C26%2C0%2C26%29%2Carrow%2816.5%2C26%2C24.142%2C26%29%2C%0D%0Aarrow%2825%2C9%2C25%2C0%29%2Carrow%2825%2C15%2C25%2C24.142%29%2Clocate%2817%2C14%2Cx%281%2Bsqrt%282%29%29%29%2C%0D%0Alocate%28-19%2C14.5%2Cx%282%2Bsqrt%282%29%29%29%2C%0D%0Aarrow%28-14%2C11.838%2C-25%2C0.838%29%2Carrow%28-11%2C14.838%2C-0.838%2C25%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > roof piece <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28150%2C300%2C-13%2C13%2C-12%2C40%2C%0D%0Atriangle%28-10%2C0%2C10%2C0%2C0%2C34.142%29%2Cgreen%28line%280%2C0%2C0%2C34.142%29%29%2C%0D%0Alocate%28-1.5%2C0%2C2x%29%2Clocate%28-4.5%2C14%2Cx%282%2Bsqrt%282%29%29%29%2C%0D%0Alocate%28-6%2C3%2Cx%29%2Clocate%284%2C3%2Cx%29%2C%0D%0Aarrow%28-1.5%2C-1.5%2C-10%2C-1.5%29%2Carrow%281.5%2C-1.5%2C10%2C-1.5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The measure of the angles at the bottom of the roof pieces should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=73.7%5Eo ALIGN=MIDDLE  ALT=\"73.7%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%2873.7%5Eo%29=2%2Bsqrt%282%29 ALIGN=MIDDLE  ALT=\"tan%2873.7%5Eo%29=2%2Bsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The other angle would measure <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32.6%5Eo ALIGN=MIDDLE  ALT=\"32.6%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "However, maybe it is easier to make the height of the triangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Bsqrt%282%29%29%2F2 ALIGN=MIDDLE  ALT=\"%282%2Bsqrt%282%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > times (about 1.707 times) the length of the base. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );