SOLUTION: From an airplane flying at an altitude of 1000m , the angle of depression to a ship is 60 degrees. \The distance from the ship to a point directly below the plane is ?

Question 180185: From an airplane flying at an altitude of 1000m , the angle of depression to a ship is 60 degrees. \The distance from the ship to a point directly below the plane is ?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
From an airplane flying at an altitude of 1000m , the angle of depression to a ship is 60 degrees. \The distance from the ship to a point directly below the plane is ?
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Draw the picture.
You have a right triangle; find the base.
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The angle of depression from the plane = the angle of elemation from the ground.
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tan(60) = altitude/base = 1000m/base
base = 1000m/tan(60) = 577.35 meters
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Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The first thing that you need to do is assume that "a point directly below the airplane" actually means "a point on the surface of the water directly below the airplane" The airplane, ship, and the point directly below the airplane on the surface form a 30-60-90 right triangle where the direct line of sight from the aircraft to the ship is the hypotenuse.

A 30-60-90 right triangle has sides that are in proportion . So if the long leg of the triangle is 1000m, then the short leg, i.e. the distance from the ship to the point on the surface is given by so the distance is:

Rationalizing the denominator:

John

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