Triangle Calculator

There are several ways to calculate the area of a triangle: 1) Using base and height: Area = 0.5 × base × height; 2) Using three sides (Heron’s formula): First calculate the semi-perimeter s = (a+b+c)/2, then Area = √(s(s-a)(s-b)(s-c)); 3) Using two sides and the included angle: Area = 0.5 × a × b × sin(C). Our calculator automatically selects the appropriate formula based on the values you provide.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It’s expressed as a² + b² = c², where c is the hypotenuse. This theorem is used to find the length of a side in a right triangle when the lengths of the other two sides are known. Our calculator uses this theorem when dealing with right triangles.

You can calculate the angles of a triangle using the Law of Cosines or the Law of Sines. The Law of Cosines states that c² = a² + b² – 2ab·cos(C), which can be rearranged to find angle C: cos(C) = (a² + b² – c²)/(2ab). The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C). Our calculator automatically uses these laws to calculate the angles when you provide the side lengths.

Our triangle calculator can handle all types of triangles including equilateral triangles (all sides equal), isosceles triangles (two sides equal), scalene triangles (all sides different), right triangles (one angle is 90°), acute triangles (all angles less than 90°), and obtuse triangles (one angle greater than 90°). The calculator automatically determines the type of triangle based on the values you provide.

The semi-perimeter of a triangle is half of its perimeter, calculated as s = (a+b+c)/2, where a, b, and c are the lengths of the sides. The semi-perimeter is particularly useful in Heron’s formula for calculating the area of a triangle when only the three side lengths are known. It’s also used in various geometric formulas and proofs related to triangles.