Triangle calculator

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

Right scalene triangle.

Sides: a = 65.73443137182   b = 36   c = 55

Area: T = 990
Perimeter: p = 156.7344313718
Semiperimeter: s = 78.36771568591

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 33.20765703151° = 33°12'24″ = 0.58795639853 rad
Angle ∠ C = γ = 56.79334296849° = 56°47'36″ = 0.99112323415 rad

Height: ha = 30.12112546082
Height: hb = 55
Height: hc = 36

Median: ma = 32.86771568591
Median: mb = 57.87105451849
Median: mc = 45.302176597

Inradius: r = 12.63328431409
Circumradius: R = 32.86771568591

Vertex coordinates: A[55; 0] B[0; 0] C[55; 36]
Centroid: CG[36.66766666667; 12]
Coordinates of the circumscribed circle: U[27.5; 18]
Coordinates of the inscribed circle: I[42.36771568591; 12.63328431409]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 146.7933429685° = 146°47'36″ = 0.58795639853 rad
∠ C' = γ' = 123.2076570315° = 123°12'24″ = 0.99112323415 rad

How did we calculate this triangle?

1. Input data entered: side b, c and angle α. 2. Calculation of the third side a 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     