Area Formulas Using Trigonometry

Trigonometry · Axiom Academy

LESSON Area Formulas Using Trigonometry Beyond the basic formula: Using sine and other trigonometric functions to find triangle areas when we know sides and angles When you know two sides and the included angle (SAS), you can find the area using this powerful formula: Where a and b are the two known sides, and C is the included angle between them. Let's see where this formula comes from by connecting it to the basic area formula. Let's see this formula in action with a concrete example. When you know all three sides (SSS) but no angles, Heron's formula gives you the area. It's ancient (discovered around 60 AD!) but still remarkably useful. Where s is the semi-perimeter (half the perimeter): The SAS formula has three equivalent forms, depending on which angle you know: These formulas are particularly useful in real-world applications like surveying, navigation, and engineering, where measuring angles is often easier than measuring heights.

This is the written version of the interactive lesson above. See the full Trigonometry course.