document.write( "Question 1205058: The angles of elevation of the top Hof a vertical pole HO are observed to be e and a from points P and Q due east and due south of the post. If the distance PQ = d, show that the height of the post is:\r
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Algebra.Com's Answer #841685 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "The toppr link that tutor ikleyn posted is riddled with errors.
\n" ); document.write( "It's shocking how professors on the toppr website have \"verified\" that solution.
\n" ); document.write( "I can possibly understand that ikleyn may have glossed over those errors, but she should be more careful next time.\r
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\n" ); document.write( "\n" ); document.write( "Here are the errors marked in red:
  • tan(alpha) = h/OA (it should be tan(alpha) = h/AP instead)
  • tan(beta) = h/OB (it should be tan(beta) = h/BP instead)
  • Since OAB is a right angled triangle (triangles OPA, OPB, and ABP are right triangles however)
  • The second to last line where it has h^2+cot^2(alpha) as part of it (it should be h^2*cot^2(alpha). Not sure where the plus sign came from).

\n" ); document.write( "Here's what it should say
\n" ); document.write( "tan(alpha) = h/AP ---> AP = h*cot(alpha)
\n" ); document.write( "tan(beta) = h/BP ----> BP = h*cot(beta)\r
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\n" ); document.write( "\n" ); document.write( "Then focus on right triangle ABP that is flat on the ground.
\n" ); document.write( "\"%28AB%29%5E2+=+%28AP%29%5E2+%2B+%28BP%29%5E2\" pythagorean theorem\r
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\n" ); document.write( "\n" ); document.write( "\"d%5E2+=+%28h%2Acot%28alpha%29%29%5E2+%2B+%28h%2Acot%28beta%29%29%5E2\"\r
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\n" ); document.write( "\n" ); document.write( "\"d%5E2+=+h%5E2%2Acot%5E2%28alpha%29+%2B+h%5E2%2Acot%5E2%28beta%29\" \r
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\n" ); document.write( "\n" ); document.write( "\"d%5E2+=+h%5E2%2A%28+cot%5E2%28alpha%29+%2B+cot%5E2%28beta%29+%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"h%5E2+=+%28d%5E2%29%2F%28+cot%5E2%28alpha%29+%2B+cot%5E2%28beta%29+%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"h+=+sqrt%28+%28d%5E2%29%2F%28+cot%5E2%28alpha%29+%2B+cot%5E2%28beta%29+%29+%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"h+=++%28sqrt%28d%5E2%29%29%2F%28+sqrt%28cot%5E2%28alpha%29+%2B+cot%5E2%28beta%29+%29+%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"h+=++d%2F%28+sqrt%28cot%5E2%28alpha%29+%2B+cot%5E2%28beta%29+%29+%29\" since d > 0
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