# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 798.9454559674   b = 582   c = 436.998773684

Area: T = 124233.1109626
Perimeter: p = 1817.942229651
Semiperimeter: s = 908.9711148257

Angle ∠ A = α = 102.33° = 102°19'48″ = 1.78659954236 rad
Angle ∠ B = β = 45.37° = 45°22'12″ = 0.79218558816 rad
Angle ∠ C = γ = 32.3° = 32°18' = 0.56437413484 rad

Height: ha = 310.9933067345
Height: hb = 426.9187902494
Height: hc = 568.5765528671

Median: ma = 324.4499393039
Median: mb = 574.4220330175
Median: mc = 663.9109970716

Inradius: r = 136.6744425656
Circumradius: R = 408.9044103574

Vertex coordinates: A[436.998773684; 0] B[0; 0] C[561.2799144125; 568.5765528671]
Centroid: CG[332.7598960322; 189.5255176224]
Coordinates of the circumscribed circle: U[218.499886842; 345.6311032199]
Coordinates of the inscribed circle: I[326.9711148257; 136.6744425656]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 77.67° = 77°40'12″ = 1.78659954236 rad
∠ B' = β' = 134.63° = 134°37'48″ = 0.79218558816 rad
∠ C' = γ' = 147.7° = 147°42' = 0.56437413484 rad

# How did we calculate this triangle?

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