document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=279149>Question 279149</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two streets meet at an angle of 52 degrees. If a triangular lot has frontages of 60 m and 65 m on the two streets, what is the perimeter of the lot? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203018 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=203018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't know if there's an easier way to do this, but this is the way I did it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let the intersection of the two streets be point A.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let the other end of the top street be point B so that the street is represented by the line segment AB.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let the other end of the bottom street be point C so that the street is represented by the line segment AC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You have a triangle called ABC where:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "angle A is 52 degrees.<BR>\n" );
document.write( "Line Segment AB is 60 meters.<BR>\n" );
document.write( "Line Segment AC is 65 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We drop a perpendicular from point B to intersect with line AC at point D.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We now have 2 triangles.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "They are ABD and BDC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since we know angle A and we know AB = 60 meters, we can find the length of the line segment BD using the formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sin(52) = BD / AB which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sin(52) = BD / 60 because BD = 60 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We solve for BD to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "BD = 60 * Sin(52) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "BD = 47.28064522\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can also solve for AD using the formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Cos(52) = AD / AB which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Cos(52) = AD / 60  because AB = 60 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We solve for AD to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "AD = 60 * Cos(52) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "AD = 36.93968852\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We now have AB and AD and BD and AC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "AB and AC were given.<BR>\n" );
document.write( "AD and BD were solved for.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We know that AC = 65 meters and we know that AC = AD + DC and we know that AD = 36.93968852 so we can solve for BC using the formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "DC = AC - AD which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "DC = 65 - 36.93968852 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "DC = 28.06031148\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since we know BD and we know DC, we can now solve for angle C.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We use the formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Tan(C) = BD / DC which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Tan(C) = 47.28064522 / 28.06031148 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Tan(C) = 1.684965088\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We take the arctan(1.684965088) to find the angle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Angle C = 59.31154245 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now that we know angle C, we can use either BD or DC to find BC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Either one will get the same answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sin(C) = BD / BC\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We solve for BC to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "BC = BD / Sin(C) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "BC = 47.28064522 / Sin(59.341154245) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "BC = 54.98036461 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We could also have used:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Cos(C) = DC / BC.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We solve for BC to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "BC = DC / Cos(C) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "BC = 28.06031148 / Cos(59.31154245) which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "BC = 54.98036461 which is the same answer we got before as it should be.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your answer is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The perimeter of the lot is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "AB + AC + BC which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "60 + 65 + 54.98036461 = 179.9803646 meters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A picture of what I just did is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/problems/279149.jpg\" alt = \"********** PICTURE DID NOT DISPLAY PROPERLY **********\" />\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The + after the number indicates a fractional part that is not shown.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the part that's missing is AD = 36+.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );