What are the main triangle types?

By sides: Equilateral (all 3 sides equal, all angles 60°). Isosceles (2 sides equal, 2 angles equal). Scalene (all sides different). By angles: Acute (all angles 90°). All triangles have interior angles summing to 180°.

How do I find the area of a triangle?

Common methods: (1) Base-height: A = (base × height) / 2. (2) Heron's formula (using all 3 sides a, b, c): s = (a+b+c)/2; A = √(s(s−a)(s−b)(s−c)). (3) Two sides and included angle: A = (1/2) × a × b × sin(C). (4) Coordinate formula (Shoelace): A = |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| / 2.

What is the Pythagorean theorem?

For right triangles: a² + b² = c² where c is the hypotenuse (longest side, opposite the right angle). Example: legs 3 and 4 → hypotenuse = √(3²+4²) = √25 = 5. Common Pythagorean triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25). To find a leg: a = √(c²−b²).

What is the Law of Sines and Law of Cosines?

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). Useful when you know two angles and one side (AAS/ASA), or two sides and an angle opposite one of them (SSA). Law of Cosines: c² = a² + b² − 2ab·cos(C). Useful when you know all three sides (SSS) or two sides and the included angle (SAS). The Pythagorean theorem is a special case of the Law of Cosines when angle C = 90°.

Triangle Calculator

Enter any two sides (a, b, c) or a side and an angle to solve the triangle. Angles are in degrees.

Triangle Formulas

Law of Cosines

c² = a² + b² − 2ab · cos(C)

Law of Sines

a / sin(A) = b / sin(B) = c / sin(C)

Area (Heron’s Formula)

s = (a+b+c)/2 Area = √(s(s−a)(s−b)(s−c))

Frequently Asked Questions

How do I find the missing angle of a triangle?

Sum of angles = 180°. If two angles are 55° and 75°: missing angle = 180° − 55° − 75° = 50°.

What is a 3-4-5 triangle?

A right triangle with legs 3 and 4 and hypotenuse 5. It satisfies the Pythagorean theorem: 3²+4²=5². Any multiple works: 6-8-10, 9-12-15. Widely used in construction to check right angles.

Angle Sum

A + B + C = 180°

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