SOLUTION: an airplane over the pacific sights an atoll at a 5 degree angle of depression. If the plane is 450 meters above water, how many kilometers is it from a point 450 meters above the

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Question 58470: an airplane over the pacific sights an atoll at a 5 degree angle of depression. If the plane is 450 meters above water, how many kilometers is it from a point 450 meters above the atoll.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
an airplane over the pacific sights an atoll at a 5ｰ
angle of depression. If the plane is 450 meters above 
water, how many kilometers is it from a point 450 
meters above the atoll.

                 x
P覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧猷
        .   5ｰ                  |
                .               |450 m
                        .       |
                                . 
                                A

Let the plane be at point P, the atoll at point A,
and let Q be the point 450 m above the atoll at A.

We want to find the distance PQ, which we will call x.


QA = 450, and it is the side opposite the 5ｰ angle in 
right triangle PQA.

PO = x = the side adjacent the 5ｰ angle in right
triangle PQA.

So since we are given the opposite side, and we want
to find the adjacent side, we use the only one of the
basic three trigonometric functions that involves the 
opposite and the adjacent, which is the tangent. So

          opp 
tan 5ｰ = -----
          adj

          450 
tan 5ｰ = -----
           x

Multiply both sides by x:

x tan 5ｰ = 450

Divide both sides by tan 5ｰ:

             450
       x = --------
            tan 5ｰ

Use a calculator

                 450
       x = --------------
             .0874886635

       x = 5142.523535

Since 450 is rounded probably to the
nearest 10 feet, we probably should round
the final answer likewise, to 5140 feet.

Edwin