The Third Angle First
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 7 of 44.
Two angles and the side between them (ASA) leaves no complete pair: the known side is across from the angle you were not given. Find that angle first, from the angle sum.
With A = 35°, B = 80° and AB = 20: 35 + 80 + z = 180 gives z = 65, the angle across from AB. Now there is a pair, and w/sin(35°) = 20/sin(65°) gives the side w = BC, about 12.66.
On the board that is two reasons: Angles in a triangle for the third angle, then Law of sines. The board may write the law with the sines on top, as sin(z°)/20 = sin(35°)/w: it is the same law turned upside down.
Challenge
In triangle ABC, A = 54°, B = 71° and the side AB between them is 8 m. Find BC, marked x, 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