document.write( "Question 1187815: On one side of a path walk is a pedestal with a flag staff on top of it. The pedestal 2m in height while the flag staff is 3m high. At the opposite edge of the path walk the pedestal flag staff subtend
\n" ); document.write( "s equal angles. Compute the width of the path walk \n" ); document.write( "
Algebra.Com's Answer #819019 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
The way I read the problem, it looks like this:
\n" ); document.write( " As seen across the walk path from an ant on the grass at the edge of the path opposite the pedestal,
\n" ); document.write( "the pedestal subtends an angle \"red%28A%29\" , and so does the flag staff.
\n" ); document.write( "With the path walk surface being horizontal, and the pedestal and flag staff being vertical,
\n" ); document.write( "I see two right triangles, sharing the path width as one leg.
\n" ); document.write( "The height of the pedestal, \"2m\" , is the other leg of one of those triangles, opposite angle \"A\" .
\n" ); document.write( "The sum of the heights of pedestal and flag staff, \"2m%2B3m=5m\" , is a leg of the other triangle, opposite angle \"2A%29\" .
\n" ); document.write( "If \"x\" path width in m, from those right triangles, we get the trigonometric ratios:
\n" ); document.write( "\"tan%28A%29=2%2Fx\" and \"tan%282A%29=5%2Fx\"
\n" ); document.write( "Substituting those tangents into the trigonometric identity \"tan%282a%29=2%2Atan%28A%29%2F%281-tan%5E2%28A%29%29\" , we get
\n" ); document.write( "\"5%2Fx\"\"%22=%22\"\"2%282%2Fx%29%2F%281-%282%2Fx%29%5E2%29\" --> \"5%2Fx\"\"%22=%22\"\"%284%2Fx%29%2F%281-4%2Fx%5E2%29\"
\n" ); document.write( "Multiplying both sides times \"x%3C%3E0\" , we get and equivalent equation:
\n" ); document.write( "\"5\"\"%22=%22\"\"%284%29%2F%281-4%2Fx%5E2%29\"
\n" ); document.write( "Assuming that \"x%3C%3E2\" so that \"1-4%2Fx%5E2%3C%3E0\" , we multiply both sides times \"1-4%2Fx%5E2\" to get the equivalent equation
\n" ); document.write( "\"5%281-4%2Fx%5E2%29\"\"%22=%22\"\"4\" --> \"5-20%2Fx%5E2=4\" --> \"5-4=20%2Fx%5E2\" --> \"1=20%2Fx%5E2\" --> \"x%5E2=20\" --> \"x=sqrt%2820%29\" --> \"x=about+4.47\"
\n" ); document.write( "The path is \"highlight%284.47m%29\" wide. \n" ); document.write( "
\n" );