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You are the captain of a yacht, the Beauty . A sudden storm rises and when it passes, you are far off the course. You radio for help, two lighthouses reply. Point Avery reports that your direction is 138.44 degrees (north is 0 degrees) and the Point Carradine reports that your direction is 196.69 degrees (again, north is 0 degrees). After consulting your maps you learn that Point Carradine is at direction 72.04 degrees from Point Avery and the distance between them is 38.15 miles. What is your distance from both point?
First I drew a triangle that had at the ship an angle of 72.04 degreees so I got mess up and want to do this problem but I dont know if it is good can you reply this?
It is important here that you draw the figure first.Originally Posted by Chuyin
Draw any vertical-horizontal crossline. Call the intersection point A, for Avery. Draw a ray or line from point A that is 138.44 degrees clockwise from the North side of the vertical axis. So this ray is in the 4th quadrant or in the southeast position.
Then, from A again, draw another ray that is 72.04 degrees clockwise from the North side. This ray is in the first quadrant or northeast position. On this ray, mark point C, for Carradine, that is supposed to be 38.15 miles from point A.
Then draw another vertical-horizontal crossline whose intersection is at point C. From this point C, draw a ray that is 196.69 degrees clockwise from the new North side. This 3rd ray should intersect the 1st ray. Call their intersection point as B. This B is supposed to be the position of your Beauty, the yacht.
So we have a triangle ABC.
We know the length of one side, the AC. AC = 38.15 miles.
We are asked to find AB and BC.
From the given directions we can get the interior angles of triangle ABC. With the 3 angles known, and that known one side, we can get the other two sides AB and BC by using the Law of Sines.
angle A = 138.44 -72.04 = 66.40 degrees. -------**
angle C = 90 -(90 -72.04) -(196.69 -180) = 90 -17.96 -16.69 = 55.35 deg --**
angle B = 180 -66.40 -55.35 = 58.25 degrees -----***
By Law of Sines,
38.15/sin(58.25deg) = AB/sin(55.35deg) = BC/sin(66.40deg) --------****
AB = [38.15/sin(58.25deg)]*sin(55.35deg) = 36.91 miles.
BC = [38.15/sin(58.25deg)]*sin(66.40deg) = 41.11 miles.
Therefore, you are 36.91 miles from Point Avery, and 41.11 miles from Point Carradine. ------------answer.