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Triangle Solver calculator →

Triangle Solver guide

The Triangle Solver calculates all three angles, the area, and the perimeter of a triangle when you provide the lengths of all three sides. It uses the Law of Cosines and Heron’s formula.

Worked examples

Solve a standard 5-6-7 triangle

  1. Enter 5 as Side a.
  2. Enter 6 as Side b.
  3. Enter 7 as Side c.
  4. Click Calculate.
Result: A = 44.42°, B = 57.12°, C = 78.46° | Area ≈ 14.6969

Using the Law of Cosines, the angles are calculated. The area is calculated using Heron’s formula.

Solve an equilateral triangle

  1. Enter 5 for all three sides (a, b, and c).
  2. Click Calculate.
Result: A = 60°, B = 60°, C = 60° | Area ≈ 10.8253

All sides are equal, so all angles are equal. Since angles sum to 180°, each is 60°.

Check if sides form a valid triangle

  1. Enter 2 as Side a.
  2. Enter 3 as Side b.
  3. Enter 10 as Side c.
  4. Click Calculate.
Result: Error: Violates Triangle Inequality Theorem

2 + 3 = 5, which is less than 10. The two shorter sides cannot reach the ends of the longest side.

Tips

  • •This tool uses the SSS (Side-Side-Side) method.
  • •The area is found using Heron’s formula, which requires the semi-perimeter.
  • •The graph will automatically classify the triangle (e.g., acute scalene, right isosceles).

Frequently asked questions

What is the Law of Cosines?
A formula used to find an angle or side in any triangle: c² = a² + b² - 2ab·cos(C). It generalizes the Pythagorean theorem.
What is Heron’s formula?
A formula to find the area of a triangle using only its side lengths: Area = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.
What is the semi-perimeter?
Half of the triangle’s perimeter, calculated as s = (a + b + c) / 2.
What is an SSS triangle?
A triangle defined by knowing the lengths of all three sides (Side-Side-Side).
What is an obtuse triangle?
A triangle with one angle greater than 90 degrees.
What is an acute triangle?
A triangle where all three angles are less than 90 degrees.
What is a scalene triangle?
A triangle where all three sides have different lengths.
Why must a triangle satisfy the Triangle Inequality Theorem?
Because if one side is longer than the sum of the other two, they cannot physically meet to close the shape.
How do the angles always sum up?
In Euclidean geometry, the sum of the interior angles of any triangle is always exactly 180 degrees.
Can the calculator handle decimal side lengths?
Yes, it supports any positive real numbers, including decimals.
Why are my angles slightly off from 180 when added together?
Due to floating-point rounding in JavaScript, the sum might be 179.999999 or 180.000001. It is mathematically exact in theory.
How do I find the height of the triangle?
Once you have the area, Height = (2 × Area) / base. The calculator provides the area, so you can easily derive the height.
What happens if I input a negative number?
The calculator will show an error. Physical side lengths must be positive.
What is a right triangle?
A triangle where one angle is exactly 90 degrees. You can use the Pythagorean theorem on it.
Can I solve a triangle if I only know two sides?
Not completely. Two sides do not lock the triangle’s shape. You need at least one angle (SAS) or all three sides (SSS).
What is the difference between SSS and SAS?
SSS means you know all three sides. SAS means you know two sides and the angle between them.
Does this tool show the steps?
It shows the final angles, area, perimeter, and classification. It does not show the step-by-step trigonometric substitution.
How is the area calculated?
The tool calculates the semi-perimeter (s), then applies Heron’s formula.
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