Pair Side With Angle
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 6 of 44.
The law of sines needs one complete pair: a side you know and the angle across from it. Find the angle across from a side by looking for the corner the side does not touch.
In triangle KLM the side KL = 16 does not touch M, so it pairs with 65°. The side y = LM does not touch K, so it pairs with 70°. The law reads y/sin(70°) = 16/sin(65°), and y is about 16.59. The 45° angle is not needed at all.
The common mistake is to pair a side with an angle at one of its ends. On the board that pairing is refused, because the law of sines is not about those parts.
Challenge
Triangle PQR has angles 48° at P, 57° at Q and 75° at R. The side QR is 20 m. Find PR, marked x, 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