The Triangle Calculator solves triangles given various combinations of sides and angles. It supports SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), and AAS (two angles and a non-included side) configurations.
Enter the known values and the calculator will find all missing sides, angles, area, and perimeter using trigonometric formulas and Heron's formula.
Your calculations will appear here
Triangles are solved using trigonometric laws. The Law of Cosines (c^2 = a^2 + b^2 - 2ab*cos(C)) relates sides and angles, generalising the Pythagorean theorem. The Law of Sines (a/sin(A) = b/sin(B) = c/sin(C)) provides another relationship.
The area of a triangle can be calculated several ways: (1/2)*base*height, (1/2)*a*b*sin(C), or Heron's formula using the semi-perimeter s: area = sqrt(s(s-a)(s-b)(s-c)).
Problem: Find the angles of a triangle with sides 3, 4, 5
Solution: cos(C) = (9 + 16 - 25) / (2*3*4) = 0, so C = 90 degrees. This is a right triangle.
Answer: Angles: 36.87 degrees, 53.13 degrees, 90 degrees
Problem: Find the area of a triangle with sides 7, 8, 9
Solution: s = (7+8+9)/2 = 12. Area = sqrt(12*5*4*3) = sqrt(720)
Answer: Area = 26.83 square units
Interactive unit circle with exact trigonometric values. Find sin, cos, tan for any angle, reference angles, and degree-radian conversions. Free, instant results.
Calculate sector area, arc length, and find missing angle or radius. Supports degrees and radians with SVG visualisation. Free online calculator.
Calculate percentages instantly. Find what percent of a number, percentage change, and percentage difference. Free, fast, no signup.
Add, subtract, multiply, and divide fractions. Simplify fractions and convert to mixed numbers. Free online fraction calculator.
Simplify ratios and find missing values in proportions. Free online ratio calculator with step-by-step results.
Calculate powers and exponents instantly. Compute base raised to any power including negative and fractional exponents. Free online tool.