Triangle calculator

Please enter what you know about the triangle:
You have entered side b, c and angle α.

Obtuse scalene triangle.

Sides: a = 31.87546171439   b = 54   c = 67

Area: T = 849.274405708
Perimeter: p = 152.8754617144
Semiperimeter: s = 76.4377308572

Angle ∠ A = α = 28° = 0.48986921906 rad
Angle ∠ B = β = 52.68882898938° = 52°41'18″ = 0.92195841359 rad
Angle ∠ C = γ = 99.31217101062° = 99°18'42″ = 1.73333163271 rad

Height: ha = 53.288842403
Height: hb = 31.45545947067
Height: hc = 25.35114643904

Median: ma = 58.72439490794
Median: mb = 44.98332814392
Median: mc = 29.04772995137

Inradius: r = 11.11107268551
Circumradius: R = 33.94773353346

Vertex coordinates: A[67; 0] B[0; 0] C[19.32108299856; 25.35114643904]
Centroid: CG[28.77436099952; 8.45504881301]
Coordinates of the circumscribed circle: U[33.5; -5.4932865948]
Coordinates of the inscribed circle: I[22.4377308572; 11.11107268551]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152° = 0.48986921906 rad
∠ B' = β' = 127.3121710106° = 127°18'42″ = 0.92195841359 rad
∠ C' = γ' = 80.68882898938° = 80°41'18″ = 1.73333163271 rad

How did we calculate this triangle?

1. Input data entered: side b, c and angle α. 2. Calculation of the third side a of the triangle using a Law of Cosines Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. 3. The triangle circumference is the sum of the lengths of its three sides 4. Semiperimeter of the triangle 5. The triangle area using Heron's formula 6. Calculate the heights of the triangle from its area. 7. Calculation of the inner angles of the triangle using a Law of Cosines     