<PRE><B>Question 1116471</B>
From a lighthouse 520m tall, a ship is observed 5740m from the coast.
:
a) Draw a diagram showing this information.
  You can do this
b) What is the change in the angle of depression after 2 minutes if the ship is traveling towards the coast at 90km/h.
:
How far does the ship travel in two minutes, in meters
90000 * {{{2/60}}} = 3000 meters
:
Find the distance from the coast after 2min
5740 - 3000 = 2740 meters
:
The lighthouse, ship, and coast form a right triangle.
The distance from the lighthouse to the ship is the hypotenuse.
let A = the interior angle formed by the height and the hypotenuse
Tan(A) = {{{5740/520}}}
A = 84.824 degrees when the ship is 5740m from the coast
and
Tan(A) = {{{2740/520}}}
A = 79.254 degrees when the ship is 2740m from the coast
therefore
84.824 - 79.254 = 5.57 degree change
:
Note these are not the angles of depression, however the change is the same as the interior angles

 
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