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Math Calculator Tools

Triangle Calculator

Calculate comprehensive triangle properties with precision. Provide at least 3 values including one side to get detailed analysis including angles, sides, area, and advanced geometric properties.

Angle Unit

Side Lengths

Side A

Side B

Side C

Angles

Angle A (°)

Angle B (°)

Angle C (°)

Understanding Triangle Calculations

What is a Triangle?

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the interior angles of any triangle is always 180 degrees (or π radians).

Triangle Calculation Methods

SSS (Side-Side-Side)

When all three sides are known, use the Law of Cosines to find all angles.

SAS (Side-Angle-Side)

When two sides and the included angle are known, use the Law of Cosines to find the third side.

AAS/ASA

When two angles and one side are known, use the Law of Sines to find the remaining sides.

Triangle Types

By Angles: Acute (all angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°)
By Sides: Equilateral (all sides equal), Isosceles (two sides equal), Scalene (all sides different)

Quick Tip: Always provide at least one side length for accurate calculations. The triangle inequality theorem states that the sum of any two sides must be greater than the third side.

Important Triangle Formulas

Area Calculations

Heron's Formula: A = √[s(s-a)(s-b)(s-c)]
Base × Height: A = ½ × base × height
Two sides + angle: A = ½ab sin(C)

Law of Cosines & Sines

Law of Cosines: c² = a² + b² - 2ab cos(C)
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Angle Sum: A + B + C = 180° (π radians)

Calculation Tips:

• Ensure at least one side length is provided for valid triangle calculations
• Double-check that your inputs satisfy the triangle inequality theorem
• Remember that the sum of any two sides must be greater than the third side
• Angles in a triangle always sum to 180° (or π radians)