Triangle Calculator

Pick what you know about the triangle. The calculator finds the missing sides and angles, the area, perimeter and whether it is acute, right or obtuse.

Solve a triangle

Area26.83281573
Perimeter
24
Sides a, b, c
7, 8, 9
Angles A, B, C
48.1897°, 58.4119°, 73.3985°
Type
scalene, acute
Height to side a
7.66651878

Working

  1. Angles from the law of cosines: cos A = (b² + c² − a²) ÷ 2bc
  2. Area from Heron’s formula: √(s(s − a)(s − b)(s − c)), s = half the perimeter

Labelling

Angle A is opposite side a, angle B opposite b, and angle C opposite c. In SAS mode, angle C is the angle between sides a and b; in ASA mode, side c lies between angles A and B.

The rules used

angles: A + B + C = 180°

law of cosines: c² = a² + b² − 2ab cos C

law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C

Heron: area = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2

Worked example

Sides 7, 8 and 9

  1. s = (7 + 8 + 9) ÷ 2 = 12
  2. Area = √(12 × 5 × 4 × 3) = √720 ≈ 26.833
  3. cos A = (8² + 9² − 7²) ÷ (2 × 8 × 9) = 96 ÷ 144 → A ≈ 48.19°

Area ≈ 26.83; angles ≈ 48.19°, 58.41°, 73.40° — an acute scalene triangle.