SOLUTION: Standing on a cliff 380 meters above the sea, Pat sees an approaching ship and measures its angle of depression, obtaining 9 degrees. a) How far from shore is the ship b) Pat

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Question 1081497: Standing on a cliff 380 meters above the sea, Pat sees an approaching ship and measures its angle of depression, obtaining 9 degrees.
a) How far from shore is the ship
b) Pat sights a second ship beyond the first. the angle of depression of the second ship is 5 degrees. How far apart are the ships?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
The angle that Pat's line of sight
makes with the horizon is also +9+ degrees
If +d+ = distance from the ship to the shore, then
+tan%28+9+%29+=+380%2Fd+
+.1584+=+380%2Fd+
+d+=+380%2F.1584+
+d+=+2399.23+
The ship is 2,399.23 meters from the shore
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(b)
For the 2nd ship:
+tan%285%29++=+380%2Fd%5B2%5D+
+.0875+=+380%2Fd%5B2%5D+
+d%5B2%5D+=+380%2F.0875+
+d%5B2%5D+=+4343.42+
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+d%5B2%5D+-+d+=+4343.42+-+2399.23+
+d%5B2%5D+-+d+=+1944.19+
The distance between the ships is 1,944.19 meters