Triangle calculator

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

Right scalene triangle.

Sides: a = 100.3821983754   b = 8.74988663526   c = 100

Area: T = 437.443331763
Perimeter: p = 209.1310850107
Semiperimeter: s = 104.5655425053

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 5° = 0.08772664626 rad
Angle ∠ C = γ = 85° = 1.48435298642 rad

Height: ha = 8.71655742748
Height: hb = 100
Height: hc = 8.74988663526

Median: ma = 50.19109918772
Median: mb = 100.09656326
Median: mc = 50.76596558544

Inradius: r = 4.18334412991
Circumradius: R = 50.19109918772

Vertex coordinates: A[100; 0] B[0; 0] C[100; 8.74988663526]
Centroid: CG[66.66766666667; 2.91662887842]
Coordinates of the circumscribed circle: U[50; 4.37444331763]
Coordinates of the inscribed circle: I[95.81765587009; 4.18334412991]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 175° = 0.08772664626 rad
∠ C' = γ' = 95° = 1.48435298642 rad

How did we calculate this triangle?

1. Input data entered: side c, angle α and angle β. 2. From angle α and angle β we calculate angle γ: 3. From angle α, angle γ and side c we calculate side a - By using the law of sines, we calculate unknown side a: 4. 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. 5. The triangle circumference is the sum of the lengths of its three sides 6. Semiperimeter of the triangle 7. The triangle area using Heron's formula 8. Calculate the heights of the triangle from its area. 9. Calculation of the inner angles of the triangle using a Law of Cosines     