Triangle calculator

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

Acute scalene triangle.

Sides: a = 65.94332984162   b = 65   c = 39

Area: T = 1218.39991996
Perimeter: p = 169.9433298416
Semiperimeter: s = 84.97216492081

Angle ∠ A = α = 74° = 1.29215436465 rad
Angle ∠ B = β = 71.35438419583° = 71°21'14″ = 1.24553594761 rad
Angle ∠ C = γ = 34.64661580417° = 34°38'46″ = 0.6054689531 rad

Height: ha = 36.95329346837
Height: hb = 37.48992061416
Height: hc = 62.4822010236

Median: ma = 42.26595592558
Median: mb = 43.34217731871
Median: mc = 62.50220743896

Inradius: r = 14.3398890806
Circumradius: R = 34.33003880706

Vertex coordinates: A[39; 0] B[0; 0] C[21.08435718719; 62.4822010236]
Centroid: CG[20.02878572906; 20.82773367453]
Coordinates of the circumscribed circle: U[19.5; 28.21881966432]
Coordinates of the inscribed circle: I[19.97216492081; 14.3398890806]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 106° = 1.29215436465 rad
∠ B' = β' = 108.6466158042° = 108°38'46″ = 1.24553594761 rad
∠ C' = γ' = 145.3543841958° = 145°21'14″ = 0.6054689531 rad

How did we calculate this triangle?

1. Input data entered: side b, c and angle α. 2. Calculation of the third side a 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. 3. The triangle circumference is the sum of the lengths of its three sides 4. Semiperimeter of the triangle 5. The triangle area using Heron's formula 6. Calculate the heights of the triangle from its area. 7. Calculation of the inner angles of the triangle using a Law of Cosines     