Triangle calculator

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

Right scalene triangle.

Sides: a = 18.78553923199   b = 18.5   c = 3.26220491431

Area: T = 30.17439545737
Perimeter: p = 40.5477441463
Semiperimeter: s = 20.27437207315

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 80° = 1.39662634016 rad
Angle ∠ C = γ = 10° = 0.17545329252 rad

Height: ha = 3.21224912868
Height: hb = 3.26220491431
Height: hc = 18.5

Median: ma = 9.39326961599
Median: mb = 9.80883364855
Median: mc = 18.57217592369

Inradius: r = 1.48883284116
Circumradius: R = 9.39326961599

Vertex coordinates: A[3.26220491431; 0] B[0; 0] C[3.26220491431; 18.5]
Centroid: CG[2.17546994287; 6.16766666667]
Coordinates of the circumscribed circle: U[1.63110245716; 9.25]
Coordinates of the inscribed circle: I[1.77437207315; 1.48883284116]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 100° = 1.39662634016 rad
∠ C' = γ' = 170° = 0.17545329252 rad

How did we calculate this triangle?

1. Input data entered: side b, angle α and angle β. 2. From angle α and angle β we calculate angle γ: 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     