Triangle calculator

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

Acute scalene triangle.

Sides: a = 430.8660000999   b = 429.1277215462   c = 66

Area: T = 14143.06326736
Perimeter: p = 925.9877216461
Semiperimeter: s = 462.9943608231

Angle ∠ A = α = 87.1° = 87°6' = 1.52201817785 rad
Angle ∠ B = β = 84.1° = 84°6' = 1.46878219009 rad
Angle ∠ C = γ = 8.8° = 8°48' = 0.15435889742 rad

Height: ha = 65.65503859297
Height: hb = 65.91554775742
Height: hc = 428.5787656777

Median: ma = 218.7330424061
Median: mb = 221.2770487114
Median: mc = 428.7266315679

Inradius: r = 30.54769933541
Circumradius: R = 215.706624315

Vertex coordinates: A[66; 0] B[0; 0] C[44.28991925028; 428.5787656777]
Centroid: CG[36.76330641676; 142.8599218926]
Coordinates of the circumscribed circle: U[33; 213.1677031536]
Coordinates of the inscribed circle: I[33.86663927683; 30.54769933541]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 92.9° = 92°54' = 1.52201817785 rad
∠ B' = β' = 95.9° = 95°54' = 1.46878219009 rad
∠ C' = γ' = 171.2° = 171°12' = 0.15435889742 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     