# 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 = 439.8387904317   b = 1286   c = 1208.445471033

Area: T = 265759.8944437
Perimeter: p = 2934.283261465
Semiperimeter: s = 1467.141130732

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 70° = 1.22217304764 rad

Height: ha = 1208.445471033
Height: hb = 413.3122433028
Height: hc = 439.8387904317

Median: ma = 1228.293270268
Median: mb = 643
Median: mc = 747.3576699679

Inradius: r = 181.1411307324
Circumradius: R = 643

Vertex coordinates: A[1208.445471033; 0] B[0; 0] C[-0; 439.8387904317]
Centroid: CG[402.8154903444; 146.6132634772]
Coordinates of the circumscribed circle: U[604.2222355165; 219.9198952158]
Coordinates of the inscribed circle: I[181.1411307324; 181.1411307324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 110° = 1.22217304764 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    