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Math

Triangle Calculator

Solve any triangle from three sides (SSS), two sides and the angle between them (SAS), or two angles and the side between them (ASA).

Rules last checked 25 October 2026Every step shown

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Area

26.8328

Sides a, b, c
7, 8, 9
Angles A, B, C
48.19°, 58.41°, 73.4°
Perimeter
24
Type
Scalene, acute

This is a scalene, acute triangle with sides 7, 8 and 9, angles 48.2°, 58.4° and 73.4°, and an area of 26.833.

How it's worked out

  1. Angles (law of cosines)cos A = (b² + c² − a²) ÷ 2bc, and so on48.19°, 58.41°, 73.4°
  2. Area (Heron's formula)s = 12; √(s(s − a)(s − b)(s − c))26.8328

The rules

Law of cosines: c² = a² + b² − 2ab cos C · Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C · Angles add up to 180°

Worked example

Sides 7, 8 and 9: the angles are 48.19°, 58.41° and 73.40°, so it's a scalene, acute triangle. With s = 12, the area is √(12 × 5 × 4 × 3) = √720 = 26.83.

Questions people ask

How do I find the angles from three sides?

Use the law of cosines: cos A = (b² + c² − a²) ÷ 2bc, and the same pattern for the other angles.

How do I find the area from three sides?

Use Heron's formula: with s half the perimeter, area = √(s(s − a)(s − b)(s − c)).

When can three lengths not make a triangle?

When one side is as long as the other two together or longer: 1, 2 and 5 can't make a triangle.

Formula and rules last checked 25 October 2026Written and tested by the CalculatorDex teamReport a problem