Triangle Side Angle
Use the ASA theorem to solve any triangle given one side and two adjacent angles. Free online triangle side angle calculator for students, teachers, and geometry professionals.
About This Calculator
This free online triangle side angle calculator solves a triangle using the ASA (Angle-Side-Angle) method. Given one side length and two adjacent angles, it computes the third angle and the remaining two side lengths using the law of sines. This is one of the most common triangle-solving scenarios in geometry and trigonometry education.
The solution follows two simple steps. First, the third angle is found using the triangle sum theorem: Angle C = 180 deg - Angle A - Angle B. Since the three interior angles of any triangle always sum to 180 degrees, knowing two angles immediately yields the third. Then, the law of sines (a/sin(A) = b/sin(B) = c/sin(C)) is applied to compute the unknown side lengths b and c from the given side a. The law of sines states that the ratio of a side length to the sine of its opposite angle is constant for all three sides of a triangle.
The ASA method is a fundamental technique in trigonometry with practical applications in surveying, where surveyors measure angles with a theodolite and use baseline distances to calculate inaccessible distances. It is also used extensively in navigation for triangulation, in engineering for structural analysis, in construction for layout and site planning, and in astronomy for measuring distances to nearby celestial objects.
Whether you are a high school geometry student learning the law of sines for the first time, a teacher preparing classroom examples, or a professional surveyor needing quick triangle solutions from angle-side-angle measurements, this calculator provides instant and accurate results. For AAS (Angle-Angle-Side) triangle solving where the known side is not between the two angles, see our dedicated AAS triangle calculator.
Frequently Asked Questions
What does the Triangle Side Angle Calculator do?
It solves a triangle when given one side length and two adjacent angles. Using the triangle sum theorem and the law of sines, it computes the third angle and the lengths of the other two sides.
What formula does this calculator use?
First it finds the third angle: C = 180 deg - A - B. Then it applies the law of sines: a/sin(A) = b/sin(B) = c/sin(C). Given side a and angles A and B, it computes side b = axsin(B)/sin(A) and side c = axsin(C)/sin(A).
What is the Angle-Side-Angle (ASA) method?
ASA (Angle-Side-Angle) is a triangle congruence condition where two angles and the included side between them are known. The third angle follows from the triangle sum theorem (180 deg), and the remaining sides are found using the law of sines.
What inputs do I need to provide?
Enter side a length, angle A (opposite side a) in degrees, and angle B (adjacent to side a) in degrees. The calculator will find angle C and sides b and c.
Is this calculator free to use?
Yes, all calculators on Calculy are completely free to use with no registration required.
What is the difference between ASA and AAS triangle solving?
In ASA (Angle-Side-Angle), the known side is between the two given angles. In AAS (Angle-Angle-Side), the known side is not between the two angles. Both methods use the triangle sum theorem to find the third angle, then the law of sines to find the unknown sides.
Can I provide angles in radians instead of degrees?
Currently this calculator accepts angles in degrees only. To convert radians to degrees, multiply by 180/pi. For example, pi/3 radians = 60 degrees.
What if angle A and angle B sum to more than 180 degrees?
If the sum of angles A and B is 180 deg or more, no valid triangle exists because the three interior angles of any triangle must sum to exactly 180 deg. The calculator will not compute results for invalid inputs.