Soluções Trigonométricas de Triângulo — Calculadora Online Grátis
Solve any triangle — sides, angles, area, perimeter (SSS, SAS, ASA, AAS)
The Triangle Calculator solves any triangle given sufficient information — three sides (SSS), two sides and an included angle (SAS), two angles and a side (ASA or AAS). It computes all missing sides and angles using the Law of Sines and Law of Cosines, plus area and perimeter. Surveyors, architects, physics students, and anyone working with oblique triangles use this regularly.
Frequently Asked Questions
Sobre Esta Calculadora
Triangles are the simplest polygon and appear throughout mathematics, engineering, and physical science. Unlike right triangles (which can be solved with the Pythagorean theorem), oblique triangles (without a 90° angle) require the Law of Sines or Law of Cosines. This calculator handles all cases: SSS (all three sides known), SAS (two sides and included angle), ASA (two angles and included side), and AAS (two angles and a non-included side).
The Law of Cosines generalizes the Pythagorean theorem to any triangle: c² = a² + b² − 2ab·cos(C). When C = 90°, cos(90°) = 0 and it reduces exactly to a² + b² = c². The Law of Sines states that the ratio of each side to the sine of its opposite angle is constant for a given triangle.
Applications include surveying land boundaries, calculating roof pitch in construction, navigation and triangulation, physics problems involving force vectors, and computer graphics where triangles are the basic rendering primitive.
Avalie a área do triângulo usando a fórmula perfeita.
Exemplo Resolvido
Solving a triangle with sides a=7, b=10, and included angle C=42°
Entradas:
- Side a = 7
- Side b = 10
- Angle C = 42° (SAS case)
Passo a Passo:
- Find side c using the Law of Cosines: c² = a² + b² − 2ab·cos(C)
- c² = 49 + 100 − 2(7)(10)·cos(42°)
- c² = 149 − 140 × 0.7431 = 149 − 104.03 = 44.97
- c = √44.97 ≈ 6.71
- Find angle A using Law of Sines: sin(A)/a = sin(C)/c
- sin(A) = 7 × sin(42°) / 6.71 = 7 × 0.6691 / 6.71 ≈ 0.6984
- A = arcsin(0.6984) ≈ 44.3°
- Angle B = 180° − 42° − 44.3° = 93.7°
- Area = ½ × a × b × sin(C) = ½ × 7 × 10 × sin(42°) = 23.4 units²