Triangle calculator

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

Acute scalene triangle.

Sides: a = 91   b = 68   c = 112.6465501543

Area: T = 3093.529876881
Perimeter: p = 271.6465501543
Semiperimeter: s = 135.8232750772

Angle ∠ A = α = 53.87438635249° = 53°52'26″ = 0.94402762993 rad
Angle ∠ B = β = 37.12661364751° = 37°7'34″ = 0.648797332 rad
Angle ∠ C = γ = 89° = 1.55333430343 rad

Height: ha = 67.99896432706
Height: hb = 90.98661402592
Height: hc = 54.92550298757

Median: ma = 81.15657423043
Median: mb = 96.5876771915
Median: mc = 57.27334471244

Inradius: r = 22.77662193833
Circumradius: R = 56.33113303061

Vertex coordinates: A[112.6465501543; 0] B[0; 0] C[72.55550900568; 54.92550298757]
Centroid: CG[61.73435305334; 18.30883432919]
Coordinates of the circumscribed circle: U[56.32327507716; 0.98331172717]
Coordinates of the inscribed circle: I[67.82327507716; 22.77662193833]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.1266136475° = 126°7'34″ = 0.94402762993 rad
∠ B' = β' = 142.8743863525° = 142°52'26″ = 0.648797332 rad
∠ C' = γ' = 91° = 1.55333430343 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     