Triangle Calculator
Solve any triangle from three sides, two sides and the angle between them, or two angles and a side — angles, area, perimeter and heights.
About this tool
Choose what you know — three sides (SSS), two sides and the angle between them (SAS), or two angles and the side between them (ASA) — and enter the values. The calculator finds the missing sides and angles with the law of cosines and the law of sines, and shows the area, the perimeter, the height to each side and whether the triangle is right, acute or obtuse.
Frequently asked questions
Use the law of cosines: cos A = (b² + c² − a²) ÷ 2bc, and the same for the other angles. For sides 5, 6 and 7, cos A = (36 + 49 − 25) ÷ 84 = 0.714, so A = 44.42°. B works out at 57.12°, and C = 180° − A − B = 78.46°.
Use Heron’s formula. Work out half the perimeter, s = (a + b + c) ÷ 2, then area = √(s(s − a)(s − b)(s − c)). For sides 5, 6 and 7: s = 9 and area = √(9 × 4 × 3 × 2) = √216 = 14.70. With a base and a height you can simply use base × height ÷ 2.
No. The longest side must be shorter than the other two added together (the triangle inequality). 3, 4 and 5 works, but 2, 3 and 6 does not, because 2 + 3 = 5 is less than 6 — the two short sides cannot meet.
Two sides and a non-included angle (SSA) is the “ambiguous case”: the same three values can fit no triangle, one triangle or two different triangles. Measure the angle between the two sides (SAS) or the third side (SSS) instead, and the triangle is fixed.
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