Triangle calculator

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

Right scalene triangle.

Sides: a = 128.1155427326   b = 495   c = 478.1333284013

Area: T = 30628.125
Perimeter: p = 1101.249871134
Semiperimeter: s = 550.6244355669

Angle ∠ A = α = 15° = 0.26217993878 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 75° = 1.3098996939 rad

Height: ha = 478.1333284013
Height: hb = 123.75
Height: hc = 128.1155427326

Median: ma = 482.4055252833
Median: mb = 247.5
Median: mc = 271.2311307262

Inradius: r = 55.62443556694
Circumradius: R = 247.5

Vertex coordinates: A[478.1333284013; 0] B[0; 0] C[-0; 128.1155427326]
Centroid: CG[159.3787761338; 42.70551424419]
Coordinates of the circumscribed circle: U[239.0676642006; 64.05877136629]
Coordinates of the inscribed circle: I[55.62443556694; 55.62443556694]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165° = 0.26217993878 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 105° = 1.3098996939 rad

How did we calculate this triangle?

1. Input data entered: side b, angle α and angle β. 2. From angle α and angle β we calculate angle γ: 3. From angle α, angle β and side b we calculate side a - By using the law of sines, we calculate unknown side a: 4. Calculation of the third side c 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     