Two Coast Stations
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 8 of 44.
Two coastguard stations see the same ship. They know the distance between them and each measures the angle between the coast and its line of sight. That is ASA: two angles and the side between.
Stations S and T are 15 km apart, with angles 62° at S and 50° at T. The ship's angle is 180° - 62° - 50°, which is 68°. The distance d = SX from S is across from T, so d/sin(50°) = 15/sin(68°), and d is about 12.39 km.
Check the answer against the picture: the side across from the smaller angle is the shorter one, and 50° is smaller than 68°, so d must be shorter than 15 km.
Challenge
Coastguard stations S and T are 12 km apart along a straight coast. A ship X is seen at 47° from the coast at S and at 76° at T. Find the distance x from T to the ship, to two decimal places, and 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