Triangle calculator

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

Right scalene triangle.

Sides: a = 68.29   b = 144.6376696934   c = 127.5

Area: T = 4353.48875
Perimeter: p = 340.4276696934
Semiperimeter: s = 170.2133348467

Angle ∠ A = α = 28.17438511597° = 28°10'26″ = 0.49217264657 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 61.82661488403° = 61°49'34″ = 1.07990698611 rad

Height: ha = 127.5
Height: hb = 60.19989341887
Height: hc = 68.29

Median: ma = 131.9932920359
Median: mb = 72.3188348467
Median: mc = 93.42215531877

Inradius: r = 25.5776651533
Circumradius: R = 72.3188348467

Vertex coordinates: A[127.5; 0] B[0; 0] C[-0; 68.29]
Centroid: CG[42.5; 22.76333333333]
Coordinates of the circumscribed circle: U[63.75; 34.145]
Coordinates of the inscribed circle: I[25.5776651533; 25.5776651533]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.826614884° = 151°49'34″ = 0.49217264657 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 118.174385116° = 118°10'26″ = 1.07990698611 rad

How did we calculate this triangle?

1. Input data entered: side a, c and angle β. 2. 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. 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     