pre-calc long 10 min problem confusing?
the pilot of an airplane flying at an altitude of 3000 feet sights two ships traveling in the same direction as teh plane. The angle of depression of the farther ship is 20 degrees and the angle of the other ship is 45 degrees.
a) construct a diagram to model this situation
b)find the distance between the ships. Round answer to nearest foot.
lol thx
i’m wondering how u did that pic
Here’s my diagram:
The line of sight (i.e.,horizontal) from the airplane is parallel to that from the boat,so by alternate interior angles,the angle of depression from the airplane is the same as the angle of elevation from the boat.
From either boat to the point directly below the airplane to the airplane itself makes a right triangle. From the perspective of the boat,the opposite side of this triangle equals 3000 feet,and the distance from the boat to the spot beneath the plane is the adjacent side.
To relate opposite and adjacent,we use tangent.
So let’s call the distance between the further boat and the spot beneath the plane D,and let’s call the distance between the closer boat and the spot beneath the plane d.
tan(20°) = 3000/D
and
tan(45°) = 3000/d
So
D = 3000/tan(20°) = 8242.4 feet
and
d = 3000/tan(45°) = 3000 feet
The distance between the two boats is the difference between the two distances,D –d. Approximately 5242 feet.
EDIT:*grin* With a tablet PC,google image search,and too much spare time. 
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