Triangle calculator - result

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

Right scalene Pythagorean triangle.

Sides: a = 3   b = 4   c = 5

Area: T = 6
Perimeter: p = 12
Semiperimeter: s = 6

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 4
Height: hb = 3
Height: hc = 2.4

Median: ma = 4.27220018727
Median: mb = 3.60655512755
Median: mc = 2.5

Inradius: r = 1
Circumradius: R = 2.5

Vertex coordinates: A[5; 0] B[0; 0] C[1.8; 2.4]
Centroid: CG[2.26766666667; 0.8]
Coordinates of the circumscribed circle: U[2.5; 0]
Coordinates of the inscribed circle: I[2; 1]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 rad

How did we calculate this triangle?

1. Input data entered: side a, c and angle γ. 2. From angle γ, side a and side c we calculate side b - by using the law of cosines and quadratic equation:  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    