Triangle calculator - result

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

Acute scalene triangle.

Sides: a = 9.62655856353   b = 22   c = 22.43300561975

Area: T = 104.273286497
Perimeter: p = 54.05656418328
Semiperimeter: s = 27.02878209164

Angle ∠ A = α = 25° = 0.4366332313 rad
Angle ∠ B = β = 75° = 1.3098996939 rad
Angle ∠ C = γ = 80° = 1.39662634016 rad

Height: ha = 21.66657705663
Height: hb = 9.47993513609
Height: hc = 9.29876017583

Median: ma = 21.68884931659
Median: mb = 13.32996112696
Median: mc = 12.74994742698

Inradius: r = 3.85879826799
Circumradius: R = 11.38880379845

Vertex coordinates: A[22.43300561975; 0] B[0; 0] C[2.49112848827; 9.29876017583]
Centroid: CG[8.30771136934; 3.09992005861]
Coordinates of the circumscribed circle: U[11.21550280987; 1.97875120432]
Coordinates of the inscribed circle: I[5.02878209164; 3.85879826799]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155° = 0.4366332313 rad
∠ B' = β' = 105° = 1.3098996939 rad
∠ C' = γ' = 100° = 1.39662634016 rad

How did we calculate this triangle?

1. Input data entered: side b, angle α and angle γ. 2. From angle α and angle γ we calculate angle β: 3. From angle α, angle β and side b we calculate side a - By using the law of sines, we calculate unknown side a: 4. Calculation of the third side c 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. 5. The triangle circumference is the sum of the lengths of its three sides 6. Semiperimeter of the triangle 7. The triangle area using Heron's formula 8. Calculate the heights of the triangle from its area. 9. Calculation of the inner angles of the triangle using a Law of Cosines     