Finding an Angle
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 10 of 44.
Two sides and an angle that is not between them (SSA) let the law of sines find a second angle. Say A = 30°, a = 8 and b = 6, and you want B. The pairs are 8 with 30° and 6 with B:
sin(B)/6 = sin(30°)/8
So sin(B) = 3/8. Between 0° and 180° two angles have that sine: about 22.02° and its supplement, about 157.98°. The second is too big: with A = 30° it would leave no room for the third angle, since 30° + 157.98° is more than 180°. So B is about 22.02°.
The board does this sorting for you. Arcsin writes both angles as cases, and an angle that leaves no triangle is ruled out on its own.
Challenge
In triangle ABC, A = 50°, a = 12 cm and b = 9 cm. Find the angle θ at B, to two decimal places, then press Check. If an angle leaves no triangle, the board rules it out.
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 Sea3The Ambiguous Case
Finding an AngleTwo TrianglesThe Height TestAn Obtuse Given AngleRadio CoverageRecap: How Many Triangles?