<PRE><B>Question 1121074</B>
you can draw triangle ABC as shown in the diagram below:


&lt;img src = &quot;http://theo.x10hosting.com/2018/080901.jpg&quot; alt=&quot;$$$&quot; &gt;


line segment AB of this triangle is equal to a distance of 110 kilometers.
point A of this triangle is one of the stations.
point B of this triangle is the other one of the stations.
point C of this triangle is the location of the ship.


the ship is 56 degrees south east of point A and 38 degrees south west of point B, as shown in the diagram.


line segment AB in the diagram is a horizontal line because it is on the east-west line of the diagram.


the vertical lines emnating from point A and B form a 90 degree with the horizontal line.


angle A of triangle ABC is therefore equal to 90 - 56 = 34 degrees.
angle B of triangle ABC is therefore equal to 90 - 38 = 52 degrees.


since the sum of the angles of a triangle is 180 degrees, that makes angle C equal to 94 degrees.


110 kilometers is opposite angle C of this triangle.
line segment b is opposite angle B of this triangle.
line segment a is opposite angle A of this triangle.


by the law of sines, 110 / sin(C) = a / sin(A) = b / sin(B)


to find a, you would take 110 / sin(C) = a / sin(A)


to find b, you would take 110 / sin(C) = b / sin(B)


solve for a to get a = 110 * sin(A) / sin(C)


solve for b to get b = 110 * sin(B) / sin(C)


these equations become:


a = 110 * sin(34) / sin(94) = 61.66142351 kilometers.


b = 110 * ain(52) / ain(94) = 86.89284951 kilometers.


b is the distance of the ship from location A.


a is the distance of the ship from location B.


a is equal to line segment BC in the diagram.


b is equal to line segment AC in the diagram.


note that a = 110 * sin(34) / sin(94) is the same as BC = 110 * sin(34) / sin(94) as shown in the diagram.


in other words, a and line segment BC are one and the same line segment.


note also that b = 110 * ain(52) / ain(94) is the same as AC = 110 * sin(52) / sin(94) as shown in the diagram.


in other words, b and line segment AC are one and the same line segment.


your solution is that the distance of the ship from point A is 86.89284951 kilometers and the distance of the ship from point B is 61.66142351 kilometers.











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