# Solutions of Triangle Calculator – SSS, SAS, ASA, AAS, and ASS

Find comprehensive solutions for triangles with our Triangle Solutions Calculator.

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To solve a triangle, you must provide three sets of information:

- Three sides (abbreviated as SSS).
- Two sides and the included angle (abbreviated as SAS).
- A side and the two angles adjacent to it (abbreviated as ASA).
- Two sides and an angle not situated between them (abbreviated as SSA).
- A side, an adjacent angle, and the opposite angle (abbreviated as AAS).

Triangles are polygons with three sides, three angles, and three vertices. They can be classified based on their side lengths and angle measurements. The most common classifications include equilateral, isosceles, scalene triangles, and right triangles.

### Equilateral Triangles

An equilateral triangle is a triangle with all three sides of equal length. Each angle in an equilateral triangle measures 60 degrees. Equilateral triangles possess symmetry and are often found in structures such as bridges and trusses.

### Isosceles Triangles

An isosceles triangle has two sides of equal length and two corresponding angles of equal measurement. The third angle in an isosceles triangle can vary. Isosceles triangles are commonly encountered in architectural designs and roof structures.

### Scalene Triangles

Scalene triangles have no equal sides or angles. All three sides and angles in a scalene triangle have different measurements. This type of triangle is frequently encountered in irregularly shaped objects and geological formations.

### Right Triangles

A right triangle contains one angle measuring 90 degrees, known as the right angle. The other two angles are acute angles, measuring less than 90 degrees. Right triangles are essential in trigonometry and have applications in fields such as navigation and construction.

## Triangle Measurement Methods

To calculate the solutions of a triangle, we need to measure various components, including sides, angles, and the area. Triangle calculators employ different methods to determine these measurements accurately. Let’s explore some of the common measurement methods used in triangle calculators.

### Side-Side-Side (SSS)

The SSS method involves measuring all three sides of a triangle. With the SSS measurements, a triangle calculator can determine the triangle’s angles and area using trigonometric functions such as the Law of Cosines and the Law of Sines.

### Side-Angle-Side (SAS)

In the SAS method, we measure one side, one angle, and another side of a triangle. The calculator employs the Law of Sines or the Law of Cosines to calculate the missing side, angles, and area.

### Angle-Side-Angle (ASA)

The ASA method requires the measurement of two angles and one side of a triangle. Triangle calculators use trigonometric functions like the Law of Sines and the Law of Cosines to find the missing side, angles, and area.

### Angle-Angle-Side (AAS)

In the AAS method, we measure two angles and one side of a triangle. The triangle calculator utilizes the Law of Sines or the Law of Cosines to calculate the missing side, angles, and area.

### Angle-Side-Side (ASS)

The ASS method involves measuring one angle and two sides of a triangle. However, this method may yield two possible solutions, depending on the angle measurement. Triangle calculators consider both solutions and provide the corresponding measurements and area.

Using triangle calculator solutions, you can solve SSS, SAS, ASA, AAS, and ASS.