Trig Triangle Calculator
Solve any triangle using ASA, SAS, or SSS methods with this free online trig triangle calculator. Find missing sides, angles, and area instantly using the law of sines and law of cosines.
About This Calculator
The Trig Triangle Calculator is a comprehensive triangle solver that uses trigonometric relationships to find all unknown sides, angles, and the area of any triangle. Whether you are a student studying trigonometry, an engineer designing structures, a surveyor measuring land, or a teacher demonstrating geometric principles, this tool handles three common triangle-solving scenarios: ASA (Angle-Side-Angle), SAS (Side-Angle-Side), and SSS (Side-Side-Side).
The calculator applies two fundamental trigonometric laws. The law of sines states that a/sin(A) = b/sin(B) = c/sin(C) for any triangle, making it ideal for ASA problems where you know two angles and the included side. The law of cosines, written as a^2 = b^2 + c^2 - 2bc·cos(A), generalizes the Pythagorean theorem to work with any triangle and is used for SAS and SSS cases. For SSS problems, the calculator also uses Heron's formula to compute the area directly from the three side lengths: area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.
This tool validates inputs before solving: angles must be positive and sum to less than 180 deg, side lengths must be positive, and the triangle inequality theorem must be satisfied for SSS inputs. Results include all three sides, all three interior angles in degrees, and the area -- all rounded to two decimal places. The calculator is part of a comprehensive collection of 2,200+ free online calculators available on Calculy for math, finance, health, and everyday use.
Frequently Asked Questions
What is a Trig Triangle Calculator?
A trig triangle calculator solves any triangle using trigonometric relationships like the law of sines and law of cosines. It accepts inputs in three modes: ASA (two angles and the included side), SAS (two sides and the included angle), and SSS (all three sides). The calculator then computes all missing sides, all three interior angles, and the total area of the triangle.
How do I solve a triangle using ASA (Angle-Side-Angle)?
In ASA mode, you enter one side length and the two adjacent angles. The calculator first finds the third angle using the triangle sum theorem (180 deg minus the sum of the two known angles). It then applies the law of sines (a/sin(A) = b/sin(B) = c/sin(C)) to compute the two remaining sides and calculates the area using 0.5 x a x b x sin(C).
How does the SAS (Side-Angle-Side) method work?
In SAS mode, you enter two side lengths and the measure of the included angle between them. The calculator uses the law of cosines (a^2 = b^2 + c^2 - 2bc·cos(A)) to find the third side. It then uses the law of cosines again to find a second angle, derives the third angle from the sum of angles, and computes the area using 0.5 x b x c x sin(A).
What is the SSS (Side-Side-Side) method?
In SSS mode, you enter all three side lengths. The calculator first verifies the triangle inequality theorem (each side must be less than the sum of the other two). It then uses the law of cosines to find each angle, and computes the area using Heron's formula: area = sqrt(s(s-a)(s-b)(s-c)) where s is the semi-perimeter.
What results does the Trig Triangle Calculator provide?
The calculator displays all three side lengths (a, b, c), all three interior angles (A, B, C) in degrees, and the total area of the triangle. All values are rounded to two decimal places for easy reading. The results update instantly when you click Solve Triangle, and the input values are saved in the URL for sharing.
What is the triangle sum theorem?
The triangle sum theorem states that the three interior angles of any triangle always add up to 180 degrees (or pi radians). This fundamental property of triangles is used by the calculator to find the third angle when two angles are known (ASA mode). It also serves as a validation check to ensure the computed angles form a valid triangle.
Can I solve right triangles with this calculator?
Yes. The trig triangle calculator works for right triangles as a special case of any triangle. In SAS mode, if the included angle is 90 deg the law of cosines reduces to the Pythagorean theorem. In SSS mode, a 3-4-5 right triangle will produce a 90 deg angle at angle C. For dedicated right triangle solving with fewer inputs, use the Right Triangle Side Angle calculator on this site.