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a cruiser is steaming on a straight course at 20 knots. An airplane, flying so low that its angle of elevation from the boat can be neglected, is traveling at 200 knots along a striaght line making a 60 degree angle with the projected course of the cruiser. Both the plane and the ship are moving in the same general direction. A battery of guns aboard the cruiser is kept trained on the plane. At the instant the guns are pointed along a line perpendicular to the path of the ship, the plane is pne half nautical mile away. The guns will start firing at the plane at the instant it is nearest the ship. What is this minimum distance, and what angle are the guns making with the path of the ship at the instance they commence firing?

So i began by using the law of Sines and found the length of all the sides and then also by graphing it by hand i found the general region where the plane would be, then also was able to find that this region was .077 nMi on the path of the ship, also labeling the angle that i needed to find as theta, or however that is spelt in english, and labeling the other unknow angle as 120 - theta. I labeled the distance as z and using the law of sines, i had set z equal to sine(60)(.077)/sin(theta) and then figuring i will take the first derivative of this and set it equal to zero, but when i do this and solve it my angle i obtain is 89.99 degress which i kno is incorrect, i was wondering if you have any suggestions on what i do because it is due this upcoming friday and i would like to be able to do it correctly to obtain a decent mark this final quarter.

thank you very much