SOLUTION: Bill and Paula, standing on the same side of land in line with the the Washington Monument, are looking at it's top. The angle of elevation from bill's position is 34.1�, and the a

Question 1036111: Bill and Paula, standing on the same side of land in line with the the Washington Monument, are looking at it's top. The angle of elevation from bill's position is 34.1�, and the angle of elevation from Paula's position is 60.0�.If bill and Paula stand on level ground an are 500 feet apart; how tall is the monument?
Answer by Aldorozos(172) (Show Source): You can put this solution on YOUR website!
Paula is closer to the monument by 500 feet. Let's assume the distance of Paula to the monument as y. Therefore the distance of Bill to the monument is 500+y
Now let's assume the height of the monument as x.
x/y = tangent of 60 = 1.732
x/(500+y) = tangent of 34.1 =.677
from the first equation we get x = y(1.732)and y = x/1.732
From the second equation we get x = (500+y)*.67 and y = x/.67 - 500
now we eliminate y by equating the two equations: x/1.732 = x/.67 - 500
Here we have everything in terms of x. We can multiply all sides of the equation by 1.732(.67). In that case we get .67x = 1.732x - 500(1.732(.67)
Now we have to solve the problem and find x.

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