# Triangle calculator

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

### Right scalene triangle.

Sides: a = 3370.164412965   b = 4472.359885626   c = 5600

Area: T = 7536291.696616
Perimeter: p = 13442.52329859
Semiperimeter: s = 6721.261149296

Angle ∠ A = α = 37° = 0.64657718232 rad
Angle ∠ B = β = 53° = 0.92550245036 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 4472.359885626
Height: hb = 3370.164412965
Height: hc = 2691.533274863

Median: ma = 4779.278769693
Median: mb = 4044.56548339
Median: mc = 2800

Inradius: r = 1121.261149296
Circumradius: R = 2800

Vertex coordinates: A[5600; 0] B[0; 0] C[2028.215540371; 2691.533274863]
Centroid: CG[2542.73884679; 897.1787582876]
Coordinates of the circumscribed circle: U[2800; 0]
Coordinates of the inscribed circle: I[2248.903263669; 1121.261149296]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143° = 0.64657718232 rad
∠ B' = β' = 127° = 0.92550245036 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: side c, angle α, angle β and angle γ. ### 2. From angle α, angle γ and side c we calculate side a - By using the law of sines, we calculate unknown side a: ### 3. Calculation of the third side b 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. ### 4. The triangle circumference is the sum of the lengths of its three sides ### 5. Semiperimeter of the triangle ### 6. The triangle area using Heron's formula ### 7. Calculate the heights of the triangle from its area. ### 8. Calculation of the inner angles of the triangle using a Law of Cosines    