Triangle calculator

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

Right scalene triangle.

Sides: a = 76.78875858022   b = 133   c = 153.5755171604

Area: T = 5106.374445585
Perimeter: p = 363.3632757407
Semiperimeter: s = 181.6811378703

Angle ∠ A = α = 30° = 0.52435987756 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 133
Height: hb = 76.78875858022
Height: hc = 66.5

Median: ma = 138.4310788965
Median: mb = 101.5880427905
Median: mc = 76.78875858022

Inradius: r = 28.10662070989
Circumradius: R = 76.78875858022

Vertex coordinates: A[153.5755171604; 0] B[0; 0] C[38.39437929011; 66.5]
Centroid: CG[63.99896548352; 22.16766666667]
Coordinates of the circumscribed circle: U[76.78875858022; 0]
Coordinates of the inscribed circle: I[48.68113787033; 28.10662070989]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150° = 0.52435987756 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 90° = 1.57107963268 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     