An Obtuse Given Angle
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 13 of 44.
When the given angle A is obtuse, the other two angles must both be acute, so there is never a second triangle. And a must be the longest side, since it is across from the largest angle. If a is not longer than b, there is no triangle at all.
With A = 120°, a = 14 and b = 10: sin(B) = 10sin(120°)/14, about 0.6186. The angles are about 38.21° and 141.79°, and 141.79° next to 120° is far over 180°. So B is about 38.21°, and the board rules out the other case itself.
Challenge
In triangle ABC, A = 110°, a = 15 cm and b = 9 cm. Find the angle θ at B, to two decimal places, then press Check.
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?