Triangle Solver Calculator

Calculate missing angles, sides, area, and other properties of a triangle based on the information you provide.

How to Use This Calculator

Enter at least three values (combination of sides and angles)
For SSS case: Enter all three sides
For SAS case: Enter two sides and the included angle
For AAS case: Enter two angles and one side
Click Calculate to see the missing values and triangle properties

Formula Used

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines: c² = a² + b² - 2ab·cos(C)

Heron's Formula: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2

Where:

a, b, c = Lengths of the triangle sides
A, B, C = Angles opposite to sides a, b, c respectively
s = Semi-perimeter of the triangle

Example Calculation

Real-World Scenario:

An architect needs to determine the angles of a triangular support beam when they know the lengths of all three sides.

Given:

Side a = 5 meters
Side b = 7 meters
Side c = 8 meters

Calculation:

Using the Law of Cosines: cos(C) = (a² + b² - c²) / (2ab)

cos(C) = (5² + 7² - 8²) / (2 × 5 × 7) = (25 + 49 - 64) / 70 = 10/70 = 0.143

C = arccos(0.143) ≈ 81.8°

Using the Law of Sines: sin(A)/a = sin(C)/c

sin(A) = a × sin(C)/c = 5 × sin(81.8°)/8 ≈ 0.618

A = arcsin(0.618) ≈ 38.2°

B = 180° - A - C = 180° - 38.2° - 81.8° = 60°

Result: The triangle has angles of approximately 38.2°, 60°, and 81.8°.

Why This Calculation Matters

Practical Applications

Architecture and construction design
Navigation and surveying
Engineering and physics calculations

Key Benefits

Solves complex triangle problems quickly
Visualizes triangle properties
Helps understand geometric relationships

Common Mistakes & Tips

A triangle cannot be uniquely determined with fewer than three pieces of information. Make sure you provide at least three values (combination of sides and angles) for accurate results.

For a valid triangle, the sum of any two sides must be greater than the third side. Additionally, the sum of all angles must equal 180°. The calculator will alert you if your inputs don't satisfy these conditions.

Frequently Asked Questions

This calculator can solve any triangle as long as you provide sufficient information. It works for acute, right, and obtuse triangles, as well as equilateral, isosceles, and scalene triangles.

You need at least three pieces of information, which can be: three sides (SSS), two sides and the included angle (SAS), two angles and one side (AAS), or two angles and the non-included side (ASA).

The calculator determines the triangle type based on side lengths and angles. If all sides are equal, it's equilateral. If two sides are equal, it's isosceles. If all sides are different, it's scalene. If one angle is 90°, it's a right triangle. If all angles are less than 90°, it's acute. If one angle is greater than 90°, it's obtuse.

References & Disclaimer

Mathematical Disclaimer

This calculator provides mathematical solutions for triangles based on the inputs provided. Results are approximations and may have small rounding errors. For critical applications, verify calculations with additional methods or consult with a qualified mathematician or engineer.

References

Law of Sines - Mathematical relationship between sides and angles of a triangle
Law of Cosines - Formula relating the lengths of the sides of a triangle to the cosine of one of its angles
Heron's Formula - Formula for finding the area of a triangle when only the lengths of the three sides are known

Accuracy Notice

This calculator provides results with precision up to 4 decimal places. For extremely small or large values, floating-point arithmetic limitations may affect accuracy. The calculator follows standard mathematical conventions for triangle calculations.

About the Author

Kumaravel Madhavan

Web developer and data researcher creating accurate, easy-to-use calculators across health, finance, education, and construction and more. Works with subject-matter experts to ensure formulas meet trusted standards like WHO, NIH, and ISO.

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