Finding a Course Angle
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 38 of 44.
Navigation also runs the other way: the distances are known from a chart and the angle to steer is wanted. That is SSS, an angle from the law of cosines, then a bearing from the angle.
From a harbour H, a buoy B is 20 km away and an island I is 14 km away, and the buoy and the island are 9 km apart. The angle φ at H between them: 9^2 = 20^2 + 14^2 - 2×20×14×cos(phi), so cos φ = 515/560 and φ is about 23.13°. If the buoy is on bearing 080° and, looking from H, the island lies to the left of it, the island is on bearing 080° − 23.13° ≈ 056.87°.
Challenge
A boat sails 30 km from harbour H to a buoy B. An island I is 25 km from H and 18 km from the buoy. Find the angle θ at H between the course to the buoy and the line to the island, to two decimal places, then press Check.
Try it yourself
Use the figure to find theta
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