Triangle Solver & Calculator

Solve triangles using the Law of Cosines and calculate comprehensive triangle properties

📐 Triangle Input

Enter two sides (a, b) and the angle between them (C) to solve the triangle

Side A (length)

Side B (length)

Angle C (degrees, between sides A and B)

💡 Example Problems

Triangle Layout

Side A opposite to angle A

Side B opposite to angle B

Side C opposite to angle C (calculated)

Angle C is between sides A and B

📊 Triangle Solution

📐

Enter two sides and the included angle to solve the triangle

📚 Triangle Properties & Formulas

Law of Cosines

c² = a² + b² - 2ab·cos(C)

Relates sides and angles in any triangle

Heron's Formula

Area = √(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2

Calculates area from three sides

Triangle Types by Angles

• Acute: All angles < 90°

• Right: One angle = 90°

• Obtuse: One angle > 90°

Triangle Types by Sides

• Equilateral: All sides equal

• Isosceles: Two sides equal

• Scalene: All sides different

Circle Properties

• Circumradius: R = abc/(4×Area)

• Inradius: r = Area/semiperimeter

Radii of circumscribed and inscribed circles

Heights (Altitudes)

Height to side = 2×Area/side_length

Perpendicular distance from vertex to opposite side

📐Formula

c² = a² + b² - 2ab·cos(C) | Area = √(s(s-a)(s-b)(s-c)) | s = (a+b+c)/2

💡How it works

The Law of Cosines relates the sides and angles of any triangle. Given two sides and the included angle, you can find the third side. Heron's formula calculates the area using all three sides.