Area With an Obtuse Angle
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 30 of 44.
The rule works the same with an obtuse angle, because sin(180° − C) = sin C. The height then falls outside the triangle, but its length is still a sin C.
Sides 8 and 5 with 120° between them: A = 1/2×8×5×sin(120°), which is 20 × √3/2 = 10√3, about 17.32. The same sides at 60° give exactly the same area: the triangle leans the other way with the same height.
The mistake to avoid is a negative area from mixing up sine and cosine: cos 120° is negative, sin 120° is not.
Challenge
Two sides of a triangle are 10 m and 6 m, and the angle between them is 150°. Find the area A exactly, then press Check.
Try it yourself
Use the figure to find A
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles Without Right Angles
4Law of Cosines: SAS
The Law of CosinesAn Obtuse Angle BetweenThrough the HillA Hooked DriveRecap: Two Sides, One Angle7Area of a Triangle
Area With a SineArea With an Obtuse AngleWorking BackwardsThe Angle From the AreaHeron's FormulaRecap: A Garden Bed2Law 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