document.write( "Question 453477: In the triangle KLM the length of KM is approximately what?: (Round to the nearest tenth)
\n" ); document.write( "KL= 7in
\n" ); document.write( "Angle M= 110 degrees
\n" ); document.write( "Angle L=30 degrees
\n" ); document.write( "

Algebra.Com's Answer #311579 by pedjajov(51)\"\" \"About 
You can put this solution on YOUR website!
If we draw a height (h) from vertex M it forms two right triangles LNM and KNM where N is a point where height h intersects KL.
\n" ); document.write( ":
\n" ); document.write( "It also divides KL into two pieces x=KN and y=LN:
\n" ); document.write( "\"x%2By=7\" -> x=7-y
\n" ); document.write( ":
\n" ); document.write( "Knowing that angle L=30 and angle M=110, it makes angle K=40.
\n" ); document.write( "Now we have:
\n" ); document.write( "\"tan%2830%29=h%2Fy\" -> h=tan(30)*y
\n" ); document.write( "\"tan%2840%29=h%2Fx\" -> h=tan(40)*x
\n" ); document.write( ":
\n" ); document.write( "\"tan%2840%29%2Ax=tan%2830%29%2Ay\", substitute x with 7-y
\n" ); document.write( "\"tan%2840%29%2A%287-y%29=tan%2830%29%2Ay\"
\n" ); document.write( "\"tan%2840%29%2A7-tan%2840%29%2Ay=tan%2830%29%2Ay\"
\n" ); document.write( "\"y=7%2Atan%2840%29%2F%28tan%2830%29%2Btan%2840%29%29\"
\n" ); document.write( "y=4.1
\n" ); document.write( ":
\n" ); document.write( "x=7-y -> x=7-4.1 -> x=2.9
\n" ); document.write( ":
\n" ); document.write( "We can find KM knowing that:
\n" ); document.write( "\"cos%2840%29=x%2FKM\"
\n" ); document.write( "\"KM=x%2Fcos%2840%29\"
\n" ); document.write( "KM=3.8\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );