Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 5.5   b = 5.82444584676   c = 10.32552432719

Area: T = 12
Perimeter: p = 21.65497017395
Semiperimeter: s = 10.82548508697

Angle ∠ A = α = 23.52204151622° = 23°31'14″ = 0.4110508686 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 131.4879584838° = 131°28'46″ = 2.29547516546 rad

Height: ha = 4.36436363636
Height: hb = 4.12105547492
Height: hc = 2.32444004396

Median: ma = 7.91986477717
Median: mb = 7.74326897912
Median: mc = 2.33112005628

Inradius: r = 1.10985603067
Circumradius: R = 6.89109214235

Vertex coordinates: A[10.32552432719; 0] B[0; 0] C[4.98546928287; 2.32444004396]
Centroid: CG[5.10333120335; 0.77548001465]
Coordinates of the circumscribed circle: U[5.1632621636; -4.56442234726]
Coordinates of the inscribed circle: I[55.0003924022; 1.10985603067]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4879584838° = 156°28'46″ = 0.4110508686 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 48.52204151622° = 48°31'14″ = 2.29547516546 rad

How did we calculate this triangle?

1. Input data entered: side a, angle β and area S. 2. From side a and angle β we calculate height hc: 3. From area T and side a we calculate height ha - The area of the triangle is the product of the length of the base and the height divided by two: 4. From area T, side a and angle β we calculate side c: 5. From area T, side a and side c we calculate side b - using Heron's formula for the area and solve of the bikvadratic 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. 6. The triangle circumference is the sum of the lengths of its three sides 7. Semiperimeter of the triangle 8. The triangle area using Heron's formula 9. Calculate the heights of the triangle from its area. 10. Calculation of the inner angles of the triangle using a Law of Cosines     