Triangle calculator ASA

Please enter the side of the triangle and two adjacent angles
°
°

Right isosceles triangle.

Sides: a = 31.82198051534   b = 31.82198051534   c = 45

Area: T = 506.25
Perimeter: p = 108.6439610307
Semiperimeter: s = 54.32198051534

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 31.82198051534
Height: hb = 31.82198051534
Height: hc = 22.5

Median: ma = 35.57656236769
Median: mb = 35.57656236769
Median: mc = 22.5

Inradius: r = 9.32198051534
Circumradius: R = 22.5

Vertex coordinates: A[45; 0] B[0; 0] C[22.5; 22.5]
Centroid: CG[22.5; 7.5]
Coordinates of the circumscribed circle: U[22.5; -0]
Coordinates of the inscribed circle: I[22.5; 9.32198051534]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 90° = 1.57107963268 rad

How did we calculate this triangle?

1. Calculate the third unknown inner angle 2. By using the law of sines, we calculate unknown side a 3. By using the law of sines, we calculate last unknown side b 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. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     