Sines or Cosines?
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 25 of 44.
Before you tap anything, ask one question: do I know a side together with the angle across from it?
Yes: use the law of sines. That covers two angles and a side (AAS and ASA, after the angle sum) and two sides with an angle across from one of them (SSA). No: use the law of cosines. That covers two sides with the angle between them (SAS) and three sides (SSS).
In triangle KLM, KL = 25, KM = 18 and K = 52°. The 52° is between the two known sides, and neither side faces a known angle: SAS. So n^2 = 25^2 + 18^2 - 2×25×18×cos(52°), and n is about 19.87.
Challenge
In triangle PQR, PQ = 23 m, QR = 31 m and the angle at Q is 47°. Find PR, marked x, to two decimal places. Choose the law yourself, 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