Triangle Calculator
About Triangle Calculator
Triangle Calculations
A triangle is a polygon with three sides and three angles that always sum to 180 degrees. Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). This calculator solves any triangle given sufficient information using the Law of Sines, Law of Cosines, and Heron's formula. Whether you need to find a missing angle, calculate the area, or determine the height, this tool handles all triangle computations.
Key Formulas
Area: A = (1/2) x base x height, or A = (1/2)ab*sin(C), or Heron's formula: A = sqrt[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2. Law of Cosines: c² = a² + b² - 2ab*cos(C). Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). These formulas allow solving any triangle when given at least three pieces of information including at least one side.
Solving Methods
SSS (three sides): Use Law of Cosines to find angles. SAS (two sides + included angle): Use Law of Cosines for the third side, then Law of Sines for remaining angles. ASA/AAS (two angles + one side): Find the third angle (sum = 180), then Law of Sines for missing sides. The calculator automatically detects which method to apply.
Frequently Asked Questions
Can a triangle have two right angles?
No. Since angles must sum to 180 degrees, two right angles (90+90=180) would leave zero degrees for the third angle. A triangle can have at most one right angle.
What is Heron's formula used for?
Heron's formula calculates the area of a triangle when you know all three sides but not the height. It uses the semi-perimeter s = (a+b+c)/2 and computes Area = sqrt[s(s-a)(s-b)(s-c)].
How do I find the height of a triangle?
Height = 2 x Area / base. First calculate the area using any method, then rearrange the basic area formula (A = 1/2 x base x height) to solve for height.
