# 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 = 654   b = 1039.216628681   c = 807.6232740374

Area: T = 264092.6366102
Perimeter: p = 2500.839902718
Semiperimeter: s = 1250.421951359

Angle ∠ A = α = 39° = 0.68106784083 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 51° = 0.89901179185 rad

Height: ha = 807.6232740374
Height: hb = 508.2533458793
Height: hc = 654

Median: ma = 871.3111362699
Median: mb = 519.6088143404
Median: mc = 768.6221898395

Inradius: r = 211.2033226782
Circumradius: R = 519.6088143404

Vertex coordinates: A[807.6232740374; 0] B[0; 0] C[-0; 654]
Centroid: CG[269.2087580125; 218]
Coordinates of the circumscribed circle: U[403.8111370187; 327]
Coordinates of the inscribed circle: I[211.2033226782; 211.2033226782]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141° = 0.68106784083 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 129° = 0.89901179185 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    