# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 46.06597304655   b = 41   c = 74.67702412564

Area: T = 833.7010726916
Perimeter: p = 161.7329971722
Semiperimeter: s = 80.86549858609

Angle ∠ A = α = 33° = 0.57659586532 rad
Angle ∠ B = β = 29° = 0.50661454831 rad
Angle ∠ C = γ = 118° = 2.05994885174 rad

Height: ha = 36.20108513072
Height: hb = 40.66883281422
Height: hc = 22.33302004356

Median: ma = 55.65992110257
Median: mb = 58.55218731547
Median: mc = 22.52441681967

Inradius: r = 10.31097863437
Circumradius: R = 42.28546394624

Vertex coordinates: A[74.67702412564; 0] B[0; 0] C[40.28547479706; 22.33302004356]
Centroid: CG[38.31883297423; 7.44334001452]
Coordinates of the circumscribed circle: U[37.33551206282; -19.85114357702]
Coordinates of the inscribed circle: I[39.86549858609; 10.31097863437]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147° = 0.57659586532 rad
∠ B' = β' = 151° = 0.50661454831 rad
∠ C' = γ' = 62° = 2.05994885174 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    