# Triangle calculator

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

### Right scalene triangle.

Sides: a = 39   b = 18.1865998668   c = 43.03217388395

Area: T = 354.6276974027
Perimeter: p = 100.2187737508
Semiperimeter: s = 50.10988687538

Angle ∠ A = α = 65° = 1.13444640138 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 18.1865998668
Height: hb = 39
Height: hc = 16.48221122079

Median: ma = 26.66442184876
Median: mb = 40.04660065036
Median: mc = 21.51658694198

Inradius: r = 7.07771299143
Circumradius: R = 21.51658694198

Vertex coordinates: A[43.03217388395; 0] B[0; 0] C[35.34660036944; 16.48221122079]
Centroid: CG[26.1265914178; 5.49440374026]
Coordinates of the circumscribed circle: U[21.51658694198; 0]
Coordinates of the inscribed circle: I[31.92328700857; 7.07771299143]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115° = 1.13444640138 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

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