Question 932230
Problem:

<img width = 800 src = "http://i.imgur.com/OImRqbV.png">


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Solution:



(a) 



Let P be the point where the plane is currently located. The length of AP is the same as the value of b (as shown below in the diagram)



<img src = "http://i150.photobucket.com/albums/s91/jim_thompson5910/16tw95xi99uci6keckw3_zps3d55d775.png">



Notice how the angle of depression corresponds to the congruent angle of elevation. Also I got the 100 degrees from the fact that 180-28-52 = 100



Use the <a href="http://www.mathsisfun.com/algebra/trig-sine-law.html">law of sines</a> to solve for b



{{{b/sin(52)=5/sin(100)}}}



{{{b=sin(52)*(5/sin(100))}}}



{{{b=4.00083544832203}}} Use a calculator here to get an approximate result



{{{b = "4.00"}}} Round to 2 decimal places



{{{b = 4}}} Drop the trailing zeros



So b is approximately <font color="red">4 miles</font>. This is the distance from point A to the plane.


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(b)


Draw in the altitude or height (shown in <font color="blue">blue</font>)


<img src = "http://i150.photobucket.com/albums/s91/jim_thompson5910/16tw95xi99uci6keckw31_zps79bd46c2.png">


Label it h for now.


Using trig, we know


{{{Sine = opposite/hypotenuse}}}



{{{sin(28) = h/b}}}



{{{sin(28) = h/4.00083544832203}}} Plug in {{{b = 4.00083544832203}}}



{{{4.00083544832203*sin(28) = h}}}



{{{h = 4.00083544832203*sin(28)}}}



{{{h = 1.87827847037293}}} Use a calculator here.



{{{h = 1.88}}} Round to 2 decimal places



The value of h is approximately 1.88 miles. 



So the elevation of the plane is approximately <font color="red">1.88 miles</font>.


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