✔ 最佳答案
Let O (the origin) be the port, A be ship A and B be ship B. So OA = 12, OB = 12, angle AOB = 30 + 90 + 30 = 150 degree.
By Cosine Rule, distance between 2 ships = AB
= sqrt [ 12^2 + 12^2 - 2(12)(12) cos 150] = sqrt ( 144 + 144 - 288 cos 150)
= sqrt (288 + 249.4) = sqrt 537.4 = 23.2 km.
(b) Since triangle AOB is an isos triangle and angle AOB = 150, so angle OBA = (180 - 150)/2 = 15 degree.
So bearing of A from B = 90 + 30 + 15 = 145 degree.
Bearing of B from A = 360 - (15 + 30) = 360 - 45 = 315 degree.
2010-08-26 04:27:16 補充：
Use following method if you don't know cosine rule: Horizontal distance between A and B = 12 cos 30 + 12 cos 60 = 16.392, vertical distance between them = 12 sin 30 + 12 cos 60 = 16.392. By Pythagoras thm., distance between them = sqrt (16.392^2 + 16.392^2) = 23.2
2010-08-26 04:28:38 補充：
Correction : Vertical distance between them should be 12 sin 30 + 12 sin 60 = 16.392.
