Triangle area (trig) Calculator
Calculate area using two sides and the included angle.
Formula first
Overview
This trigonometric formula calculates the area of a triangle by using the lengths of two sides and the sine of the angle formed between them. It is an extension of the geometric area formula, substituting the perpendicular height with the product of one side and the sine of the included angle.
Symbols
Variables
a = Side a, b = Side b, C = Angle C, A = Area
Apply it well
When To Use
When to use: Apply this formula when you are dealing with a Side-Angle-Side (SAS) scenario where the altitude of the triangle is unknown. It is the most efficient method for finding the area of non-right triangles when at least one interior angle is provided.
Why it matters: This equation is essential in land surveying and civil engineering for calculating acreage when only boundary lengths and corner angles can be measured. It also underpins the Law of Sines and provides a critical link between linear measurements and angular geometry in various scientific fields.
Avoid these traps
Common Mistakes
- Using non-included angle.
- Forgetting the 1/2.
One free problem
Practice Problem
A triangular garden plot has two sides of length 10 meters and 12 meters. If the angle between these two sides is 30°, what is the area of the garden?
Solve for:
Hint: Apply the formula directly and remember that the sine of 30° is 0.5.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Area of a triangle
- Britannica: Triangle
- Halliday, Resnick, and Walker, Fundamentals of Physics, 11th ed.
- Bird, Stewart, and Lightfoot, Transport Phenomena, 2nd ed.
- IUPAC Gold Book: Radian
- Wikipedia: Radian
- Wikipedia: Triangle
- Britannica: Euclidean geometry