document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468811>Question 468811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the side of a triangle are 70 cm, 80cm and 90cm. compute the lenght of the altitude to the 80 cm side. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321640 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The altitude or height is always perpendicular to the opposite side.<BR>\n" );
document.write( "Thus the altitude splits the triangle into 2 right triangles, of which the 2 hypotenuse sides are 70 and 90.<BR>\n" );
document.write( "Let the vertices of one of the right triangles be ABC.<BR>\n" );
document.write( "where AB = 70, BC = height<BR>\n" );
document.write( "Using trig relationships:<BR>\n" );
document.write( "sin(A) = height/70<BR>\n" );
document.write( "=> height = 70*sin(A)<BR>\n" );
document.write( "Now just find the measure of angle A by using the Law of Cosines:<BR>\n" );
document.write( "90^2 = 70^2 + 80^2 - 2(70)(80)cos(A)<BR>\n" );
document.write( "=> cos(A) = 0.2857<BR>\n" );
document.write( "=> A = cos^-1(.2857) = 73.4<BR>\n" );
document.write( "Substitute this value in for A to solve for height<BR>\n" );
document.write( "=> height = 70*sin(73.4)<BR>\n" );
document.write( "=> height = 67.1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );