Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 20.5   b = 35   c = 52.49900858932

Area: T = 227.3798505803
Perimeter: p = 107.9990085893
Semiperimeter: s = 53.99550429466

Angle ∠ A = α = 14.33216084388° = 14°19'54″ = 0.25501337544 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 140.6688391561° = 140°40'6″ = 2.45551265862 rad

Height: ha = 22.18332688588
Height: hb = 12.99330574744
Height: hc = 8.66436743657

Median: ma = 43.41770710497
Median: mb = 35.79877591273
Median: mc = 11.56881770703

Inradius: r = 4.21110996379
Circumradius: R = 41.40985277052

Vertex coordinates: A[52.49900858932; 0] B[0; 0] C[18.57993096343; 8.66436743657]
Centroid: CG[23.69897985092; 2.88878914552]
Coordinates of the circumscribed circle: U[26.24550429466; -32.02991100008]
Coordinates of the inscribed circle: I[18.99550429466; 4.21110996379]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.6688391561° = 165°40'6″ = 0.25501337544 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 39.33216084388° = 39°19'54″ = 2.45551265862 rad

How did we calculate this triangle?

1. Input data entered: side a, b and angle β. 2. From angle β, side a and side b we calculate side c - 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     