document.write( "Question 1036186: Find Height of Arch $\"some$ \n" ); document.write( "

Algebra.Com's Answer #650831 by robertb(5830) $\"\"$ $\"About$

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Let x = the distance of the foot of the axis of the arch from the vertex of angle $\"80%5Eo\"$ .\r
\n" ); document.write( "\n" ); document.write( "Then $\"tan80%5Eo+=+h%2Fx\"$ , and $\"tan69%5Eo+=+h%2F%28x%2B131%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "The first equation gives $\"x+=+h%2Ftan80%5Eo\"$ .\r
\n" ); document.write( "\n" ); document.write( "Substituting this into the 2nd equation gives\r
\n" ); document.write( "\n" ); document.write( " $\"tan69%5Eo+=+h%2F%28h%2Ftan80%5Eo+%2B131%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "==> $\"tan69%5Eo+=+%28htan80%5Eo%29%2F%28h%2B131tan80%5Eo%29\"$ \r
\n" ); document.write( "\n" ); document.write( "==> $\"htan69%5Eo+%2B+131%2Atan80%5Eo%2Atan69%5Eo+=+htan80%5Eo\"$ \r
\n" ); document.write( "\n" ); document.write( "==> $\"h+=+%28131%2Atan80%5Eo%2Atan69%5Eo%29%2F%28tan80%5Eo+-+tan69%5Eo%29+=+631.2\"$ feet, the height of the Gateway Arch. \n" ); document.write( "

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