Area With a Sine
Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 29 of 44.
Area is half the base times the height. Without a right angle the height is not given, but a sine finds it. Take sides a and b with the angle C between them, and lay b along the base. The height is the side opposite C in a right triangle with hypotenuse a, so it is a×sin(C).
A = 1/2×a×b×sin(C)
Sides 4 and 9 with 30° between them: A = 1/2×4×9×sin(30°), which is 18 × 1/2 = 9 square units. The angle must be the one between the two sides you multiply. On the board, tap the angle, both sides and the area label, then pick Area with a sine.
Challenge
Two sides of a triangle are 11 cm and 7 cm, and the angle between them is 38°. Find the area A, to two decimal places, 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