# Triangle calculator

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

### Acute scalene triangle.

Sides: a = 80   b = 104   c = 82.39772850214

Area: T = 3242.046593411
Perimeter: p = 266.3977285021
Semiperimeter: s = 133.1998642511

Angle ∠ A = α = 49.17109561152° = 49°10'15″ = 0.85881950806 rad
Angle ∠ B = β = 79.62990438848° = 79°37'45″ = 1.3989788996 rad
Angle ∠ C = γ = 51.2° = 51°12' = 0.8943608577 rad

Height: ha = 81.05111483529
Height: hb = 62.34770371945
Height: hc = 78.69330281325

Median: ma = 84.86884646347
Median: mb = 62.37551255666
Median: mc = 83.13304508305

Inradius: r = 24.34399322471
Circumradius: R = 52.86436411474

Vertex coordinates: A[82.39772850214; 0] B[0; 0] C[14.40216430777; 78.69330281325]
Centroid: CG[32.26663093664; 26.23110093775]
Coordinates of the circumscribed circle: U[41.19986425107; 33.12545590256]
Coordinates of the inscribed circle: I[29.19986425107; 24.34399322471]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.8299043885° = 130°49'45″ = 0.85881950806 rad
∠ B' = β' = 100.3710956115° = 100°22'15″ = 1.3989788996 rad
∠ C' = γ' = 128.8° = 128°48' = 0.8943608577 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle γ. ### 2. 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. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines    