SOLUTION: Two coast guard stations, A and B are on an east-west line and are 76 km apart. The bearing of a ship from station A is N 49o E and the bearing of the same ship from station B is

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Question 1121308: Two coast guard stations, A and B are on an east-west line and are 76 km apart. The bearing of a ship from station A is N 49o E and the bearing of the same ship from station B is N 61o W. If the ship gets an emergency call that a capsized vessel is somewhere between the two coast guard stations and the ship, find the area of ocean that the ship must search to find the capsized vessel.
Round your answer to two decimal places.
Answer by solver91311(24713) About Me  (Show Source):
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Since the ship bears N49°E of A, angle A of the triangle must be 41°. Likewise, based on the bearing of the ship from B, angle B of the triangle must be 29°. Then, because the sum of the angles in any triangle is 180°, the third angle of the triangle must be 110°.

Use the Law of Sines to calculate the distance from A to the Ship, hereafter .



Construct the NS line through the Ship to create a right triangle where is the hypotenuse and angle A is one of the acute angles.

Then the distance from the ship to the EW line that we will call is the height of triangle ASB. Calculate by:



Once you have calculated , calculate the desired area by:






John

My calculator said it, I believe it, that settles it