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F3 -F 4 Maths

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The other question...3.Two ships A and B leave a port at the same time.Ship A sails on a bearing of 300 degree for 12km while ship B sails on a bearing of 150 degree for 12 m.Finda)the distance between the two ships, ( answer:23.2 km)b)the bearing of ship A from ship B, (anwer:315 degree)c)the bearing of... 顯示更多 The other question... 3.Two ships A and B leave a port at the same time.Ship A sails on a bearing of 300 degree for 12km while ship B sails on a bearing of 150 degree for 12 m.Find a)the distance between the two ships, ( answer:23.2 km) b)the bearing of ship A from ship B, (anwer:315 degree) c)the bearing of ship B from ship A. (anwer:135 degree)

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A sails on a bearing of 300 degree for 12km while ship B sails on a bearing of 150 degree for 12 (km) <--- is this km or m? I'll just take it as km. a)Angle made by the paths of the ships = (300 - 150) degree = 150 degree Let y km be the distance between the two ships. By the Cosine Law, y^2 = 12^2 + 12^2 - 2(12)(12)(cos 150) y^2 = 288 + 144sqrt(3) y = 23.18221983 So the distance between the two ships is 23.2 km (corr. to 3 sig. fig.) b)Let C be the port. angle CBA = angle CAB (base angles, isos. triangle) =(180 - 150)/2 degree =15 degree So the bearing of A from B = (180 + 150 - 15) degree (refer to the fig linked below) = 315 degree c) The bearing of B from A = The bearing of A from B - 180 degree = 135 degree fig:http://i207.photobucket.com/albums/bb173/kkkpopup/fig6.jpg

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