# Triangle calculator

You have entered side c, angle α, angle β and angle γ.

### Acute scalene triangle.

Sides: a = 44.44774045078   b = 59.08334825345   c = 56

Area: T = 1176.724370478
Perimeter: p = 159.5310887042
Semiperimeter: s = 79.76554435211

Angle ∠ A = α = 45.34404620062° = 45°20'26″ = 0.79113403464 rad
Angle ∠ B = β = 71° = 1.23991837689 rad
Angle ∠ C = γ = 63.66595379938° = 63°39'34″ = 1.11110685383 rad

Height: ha = 52.94990402336
Height: hb = 39.83325777121
Height: hc = 42.02658465993

Median: ma = 53.09993033131
Median: mb = 41.02552532794
Median: mc = 44.15499132269

Vertex coordinates: A[56; 0] B[0; 0] C[14.4710659456; 42.02658465993]
Centroid: CG[23.49902198187; 14.00986155331]
Coordinates of the circumscribed circle: U[28; 13.86330739441]
Coordinates of the inscribed circle: I[20.68219609866; 14.75222994023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.6659537994° = 134°39'34″ = 0.79113403464 rad
∠ B' = β' = 109° = 1.23991837689 rad
∠ C' = γ' = 116.3440462006° = 116°20'26″ = 1.11110685383 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
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