Triangle calculator

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

Acute isosceles triangle.

Sides: a = 5.5   b = 2.38108357533   c = 5.5

Area: T = 6.39221012088
Perimeter: p = 13.38108357533
Semiperimeter: s = 6.69904178767

Angle ∠ A = α = 77.5° = 77°30' = 1.35326301703 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 77.5° = 77°30' = 1.35326301703 rad

Height: ha = 2.32444004396
Height: hb = 5.37696280392
Height: hc = 2.32444004396

Median: ma = 3.22443897783
Median: mb = 5.37696280392
Median: mc = 3.22443897783

Inradius: r = 0.9555411355
Circumradius: R = 2.81767686644

Vertex coordinates: A[5.5; 0] B[0; 0] C[4.98546928287; 2.32444004396]
Centroid: CG[3.49548976096; 0.77548001465]
Coordinates of the circumscribed circle: U[2.75; 0.61096603223]
Coordinates of the inscribed circle: I[4.31095821233; 0.9555411355]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 102.5° = 102°30' = 1.35326301703 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 102.5° = 102°30' = 1.35326301703 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     