Question 857131
Problem:


<img src = "http://i.imgur.com/HAVBuPn.png">


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Steps: 



Let x = horizontal distance between airport and plane



First mark the angle of depression (in red). That is given to be 34 degrees


<img src = "http://i.imgur.com/vq54zA5.png">


The second angle below that is also marked is congruent to the first one marked. The two angles are alternate interior angles (because of the parallel horizontal lines).


<img src = "http://i.imgur.com/BsY2udn.png">


So therefore, the bottom red angle is also 34 degrees. Let's add in the label 'x' as well so we know which side we're solving for.

<img src = "http://i.imgur.com/lnjBxfs.png">


So we have a right triangle with an angle of 34 degrees. The side opposite this angle is 3200 ft. The unknown side is the adjacent side and it is x feet long.



This means we use the tangent function



{{{Tangent = (Opposite)/(Adjacent)}}}



{{{tan(angle) = (Opposite)/(Adjacent)}}}



{{{tan(34) = (Opposite)/(Adjacent)}}}



{{{tan(34) = 3200/x}}}



{{{x*tan(34) = 3200}}}



{{{x = 3200/tan(34)}}}



{{{x = 4744.19509924}}} Use a <a href="https://www.google.com/search?q=3200%2Ftan%2834+degrees%29">calculator</a> here



{{{x = 4744}}} Round to the nearest foot



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Final Answer:



To the nearest whole foot, the approximate horizontal distance between the airport and the plane is <font color="red">4,744 feet</font>