Two Ships From Port
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 36 of 44.
Two ships leave a port at the same time on different bearings. The angle between their courses is the difference of the bearings (or 360° minus it, when the courses lie either side of north and the difference is over 180°), and after a while the distance between them is the third side of a triangle.
One ship sails 20 km on bearing 030°, the other 26 km on bearing 100°. The angle between the courses is 100° − 30° = 70° (adjacent angles at the port), so d^2 = 20^2 + 26^2 - 2×20×26×cos(70°) and the ships are about 26.84 km apart.
Challenge
Two ships leave port P at noon: one on bearing 040° at 18 km/h, the other on bearing 115° at 24 km/h. At 2 pm they are 36 km and 48 km from P. Find the distance x between them, to two decimal places, then press Check.
Try it yourself
Use the figure to find x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles Without Right Angles
2Law of Sines: AAS and ASA
Why the Law of Sines HoldsPair Side With AngleThe Third Angle FirstTwo Coast StationsRecap: Law of Sines8Bearings and Navigation
Reading BearingsTwo Ships From PortTurning Off CourseFinding a Course AngleRecap: Ships at Sea