Triangle calculator

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

Triangle has two solutions: a=3.86994850299; b=8.1; c=10.6 and a=12.08217110387; b=8.1; c=10.6.

#1 Obtuse scalene triangle.

Sides: a = 3.86994850299   b = 8.1   c = 10.6

Area: T = 13.50985817281
Perimeter: p = 22.56994850299
Semiperimeter: s = 11.2854742515

Angle ∠ A = α = 18.341061001° = 18°20'26″ = 0.32201040315 rad
Angle ∠ B = β = 41.2° = 41°12' = 0.71990756518 rad
Angle ∠ C = γ = 120.459938999° = 120°27'34″ = 2.10224129703 rad

Height: ha = 6.98221082773
Height: hb = 3.33554522785
Height: hc = 2.54987890053

Median: ma = 9.23326470419
Median: mb = 6.87548787043
Median: mc = 3.49330584304

Inradius: r = 1.19770660128
Circumradius: R = 6.1498572651

Vertex coordinates: A[10.6; 0] B[0; 0] C[2.91114582263; 2.54987890053]
Centroid: CG[4.50438194088; 0.85495963351]
Coordinates of the circumscribed circle: U[5.3; -3.11768807556]
Coordinates of the inscribed circle: I[3.1854742515; 1.19770660128]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.659938999° = 161°39'34″ = 0.32201040315 rad
∠ B' = β' = 138.8° = 138°48' = 0.71990756518 rad
∠ C' = γ' = 59.541061001° = 59°32'26″ = 2.10224129703 rad

How did we calculate this triangle?

1. Input data entered: side b, c and angle β. 2. From angle β, side c and side b we calculate side a - by using the law of cosines and quadratic equation:  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    10. Calculation of medians #2 Acute scalene triangle.

Sides: a = 12.08217110387   b = 8.1   c = 10.6

Area: T = 42.17879073232
Perimeter: p = 30.78217110387
Semiperimeter: s = 15.39108555193

Angle ∠ A = α = 79.259938999° = 79°15'34″ = 1.38333373184 rad
Angle ∠ B = β = 41.2° = 41°12' = 0.71990756518 rad
Angle ∠ C = γ = 59.541061001° = 59°32'26″ = 1.03991796833 rad

Height: ha = 6.98221082773
Height: hb = 10.41442981045
Height: hc = 7.95880957214

Median: ma = 7.24552097688
Median: mb = 10.61989157079
Median: mc = 8.81546962971

Inradius: r = 2.74404524245
Circumradius: R = 6.1498572651

Vertex coordinates: A[10.6; 0] B[0; 0] C[9.09904595105; 7.95880957214]
Centroid: CG[6.56334865035; 2.65326985738]
Coordinates of the circumscribed circle: U[5.3; 3.11768807556]
Coordinates of the inscribed circle: I[7.29108555193; 2.74404524245]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.741061001° = 100°44'26″ = 1.38333373184 rad
∠ B' = β' = 138.8° = 138°48' = 0.71990756518 rad
∠ C' = γ' = 120.459938999° = 120°27'34″ = 1.03991796833 rad

How did we calculate this triangle?

1. Input data entered: side b, c and angle β. 2. From angle β, side c and side b we calculate side a - by using the law of cosines and quadratic equation:  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     