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.
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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)).
Problema: Find the angles of a triangle with sides 3, 4, 5
Solucion: cos(C) = (9 + 16 - 25) / (2*3*4) = 0, so C = 90 degrees. This is a right triangle.
Respuesta: Angles: 36.87 degrees, 53.13 degrees, 90 degrees
Problema: Find the area of a triangle with sides 7, 8, 9
Solucion: s = (7+8+9)/2 = 12. Area = sqrt(12*5*4*3) = sqrt(720)
Respuesta: Area = 26.83 square units
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