Algebra.Com's Answer #159327 by Theo(13342)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
let angle A be the angle of elevation. This would be 43.2 degrees.
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document.write( "let angle B be the angle of depression. This would be 51.4 degrees.
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document.write( "let d be the distance between the buildings.
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document.write( "let h be the height of the office building.
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document.write( "let x be the height of the building from the point of observation up to the angle of elevation.
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document.write( "let y be the height of the building from the point of observation down. to the angle of depression.
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document.write( "tan(A) = x/d
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document.write( "tan(B) = y/d
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document.write( "x + y = h = 847
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document.write( "x = d*tan(A)
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document.write( "y = d*tan(B)
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document.write( "847 = d*tan(A) + d*tan(B)= d*(tan(A) + tan(B))
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document.write( "solving for d, you got:
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document.write( "d = 847 / (tan(A) + tan(B))
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document.write( "this became:
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document.write( "d = 847 / (tan(43.2) + tan(51.6))
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document.write( "which became:
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document.write( "d = 384.8690563
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document.write( "which became:
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document.write( "d = 385 feet to the nearest foot.
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document.write( "from that you were able to derive x and y.
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document.write( "the second part of this is asking you to show that h = d/(cot(A) + cot(B))
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document.write( "i don't think this equation is accurate.
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document.write( "here's my reasoning.
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document.write( "from h = d * (tan(A) + tan(B)) you were able to derive d = h / (tan(A) + tan(B)) and get a solution that made sense.
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document.write( "from that same equation, i could NOT derive:
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document.write( "h = d/(cot(A) + cot(B))
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document.write( "i assumed that equation was right, and could NOT derive a known h from a known d and a known A and a known B.
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document.write( "in other words, that equation is not accurate.
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document.write( "from h = d * (tan(A) + tan(B)) i was able to derive:
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document.write( "h = d/cot(A) + d/cot(B) which i proved WAS accurate by substituting known values for d, h, A, and B.
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document.write( "taking the known equation of h = d * (tan(A) + tan(B)), the best i could do was:
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document.write( "h = d (cot(A) + cot(B))/(cot(A)*cot(B))
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document.write( "this was equivalent to:
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document.write( "h = d/cot(A) + d/cot(B)
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document.write( "in other words, i don't think you have the right equation for problem number 34.
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document.write( "i also went back to your original problem and solved for h using cotangent rather than tangent.
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document.write( "the equation i got was:
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document.write( "h = d/cot(A) + d/cot(B) which is NOT equal to d/(cot(A) + cot(B))
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document.write( "P.S.
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document.write( "a picture of how i viewed this problem can be found on my website at:
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document.write( "http://theo.x10hosting.com/
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document.write( "look for problem number 210922.
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document.write( "if it's not there, wait 30 minutes and try again.
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