Maths Geometry

Triangle calculator

Mode

Side a

Side b

Hypotenuse 5

√(3² + 4²)

Area 6

Perimeter 12

Angle opposite a 36.8699°

Angle opposite b 53.1301°

Each side must be shorter than the other two

For a right triangle, the hypotenuse is √(a² + b²) — a 3 and 4 give 5. For any triangle with three known sides, Heron’s formula gives the area from the semi-perimeter, and the cosine rule gives the angles.

How to solve a triangle

1 Choose whether you have a right angle and two sides, or three sides.

2 Enter the lengths in any consistent unit.

3 Read the missing side or the area, plus every angle.

4 Check the type row — it tells you if the sides cannot form a triangle at all.

Heron formula is remarkable for needing no angle and no height: from the semi-perimeter s, the area is √(s(s−a)(s−b)(s−c)). It has been known for two thousand years and it is still the fastest route to the area of a triangle you have measured with a tape rather than drawn. The cosine rule then recovers every angle, so three tape measurements fully determine the shape.

Questions

How do I find the hypotenuse? −

Square both other sides, add them, take the square root. 3 and 4 give 5.

What is Heron's formula? +

When do three lengths not form a triangle? +

How do I check a corner is square? +

Do the angles always add to 180? +

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