Triangle calculator

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

Acute scalene triangle.

Sides: a = 36   b = 37.73768234214   c = 41.25882417879

Area: T = 629.8021521181
Perimeter: p = 114.9955065209
Semiperimeter: s = 57.49875326046

Angle ∠ A = α = 54° = 0.94224777961 rad
Angle ∠ B = β = 58° = 1.01222909662 rad
Angle ∠ C = γ = 68° = 1.18768238914 rad

Height: ha = 34.9898973399
Height: hb = 33.37986187644
Height: hc = 30.53297314616

Median: ma = 35.20216360228
Median: mb = 33.8109825454
Median: mc = 30.56991558947

Inradius: r = 10.95435399634
Circumradius: R = 22.2499223595

Vertex coordinates: A[41.25882417879; 0] B[0; 0] C[19.07770935124; 30.53297314616]
Centroid: CG[20.11217784334; 10.17765771539]
Coordinates of the circumscribed circle: U[20.62991208939; 8.33547058571]
Coordinates of the inscribed circle: I[19.76107091832; 10.95435399634]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126° = 0.94224777961 rad
∠ B' = β' = 122° = 1.01222909662 rad
∠ C' = γ' = 112° = 1.18768238914 rad

How did we calculate this triangle?

1. Input data entered: side a, angle α and angle γ. 2. From angle α and angle γ we calculate angle β: 3. From angle β, angle α and side a we calculate side b - By using the law of sines, we calculate unknown side b: 4. From angle γ, angle α and side a we calculate side c - By using the law of sines, we calculate unknown side c: 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     