How to solve a triangle
- Choose the data you have: three sides, two sides and an angle, two angles and a side, or the legs.
- Enter the values; angles are in degrees.
- See the area, the perimeter and the missing sides and angles.
- Also check the heights, the radii and the type of triangle, and tap “Copy result”.
How a triangle is solved
With three sides (SSS) the law of cosines gives the angles and Heron's formula gives the area. With two sides and the angle between them (SAS) the third side comes from the law of cosines. With two angles and a side (AAS) the third angle is 180° minus the other two and the sides come from the law of sines.
Example: the triangle with sides 3, 4 and 5 is a right triangle. Its angles are 36.87°, 53.13° and 90°, the area is 6, the perimeter is 12, the radius of the inscribed circle is 1 and that of the circumscribed circle is 2.5. In a right triangle with legs 5 and 12, the hypotenuse is 13.
Good to know
- With two sides and an angle that is not between them (SSA) there can be two solutions, which is why that combination is not offered.
- The angles of a triangle add up to 180°.
- Measurements are not converted: use the same unit for all the sides. The area is in that unit squared.
Frequently asked questions
How do I calculate the area of a triangle from its three sides?
With Heron's formula: calculate the semiperimeter s and the area is √(s(s−a)(s−b)(s−c)). The tool does it for you.
How do I find the hypotenuse?
Choose “Right triangle (legs)” and enter the two legs: the hypotenuse is the square root of the sum of their squares (Pythagorean theorem).
What does “No triangle exists” mean?
That the data is impossible: for example, one side longer than the sum of the other two, or angles that add up to 180° or more.
How do I know if it is equilateral, isosceles or scalene?
The “Type of triangle” result shows it, along with whether it is acute, right or obtuse.
Are my measurements saved?
No. Everything is calculated in your browser.