SOLUTION: Two ships are out in a storm in the ocean. The captain of the ship that is farthest out sees a lighthouse on shore. The angle of elevation in looking to the top of the lighthouse i
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Question 973143: Two ships are out in a storm in the ocean. The captain of the ship that is farthest out sees a lighthouse on shore. The angle of elevation in looking to the top of the lighthouse is 4 degrees. The light house is 100 m in height.From a second ship that is closer to the lighthouse the angle of elevation looking up at the tower is 6 degrees. Use this information to determine how far apart the two ships are.Please draw a diagram also.
Thanks :)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two ships are out in a storm in the ocean.
The captain of the ship that is farthest out sees a lighthouse on shore.
The angle of elevation in looking to the top of the lighthouse is 4 degrees.
The light house is 100 m in height.
From a second ship that is closer to the lighthouse the angle of elevation looking up at the tower is 6 degrees.
Use this information to determine how far apart the two ships
=
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=
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100
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_________a__________6\______________4\______
|-------------------------A---------------------------|
You find the leg of each right triangle using the law of sines
:
The small triangle, find the 3rd angle 180 - 90 - 6 = 94
=
=
cross multiply
.10453a = 100*.99756
a =
a = 954.3 m from the lighthouse is the nearby ship
:
The larger triangle, find the 3rd angle 180 - 90 - 4 = 96
=
=
cross multiply
.069756A = 100*.99452
A =
A = 1430.1 m from the lighthouse is the further ship
:
The distance between the ships: 1430.1 - 954.3 = 475.8 meters
:
You better check my math here.
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