Triangle calculator

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

Acute scalene triangle.

Sides: a = 15.4   b = 25.8   c = 27.25875591413

Area: T = 194.6600319381
Perimeter: p = 68.45875591413
Semiperimeter: s = 34.22987795707

Angle ∠ A = α = 33.60330112752° = 33°36'11″ = 0.58664831853 rad
Angle ∠ B = β = 68° = 1.18768238914 rad
Angle ∠ C = γ = 78.39769887248° = 78°23'49″ = 1.36882855769 rad

Height: ha = 25.27327687507
Height: hb = 15.0855296076
Height: hc = 14.27986313603

Median: ma = 25.39771901039
Median: mb = 17.9990477069
Median: mc = 16.29989682929

Inradius: r = 5.6855283607
Circumradius: R = 13.91330981805

Vertex coordinates: A[27.25875591413; 0] B[0; 0] C[5.76989415386; 14.27986313603]
Centroid: CG[11.009883356; 4.76595437868]
Coordinates of the circumscribed circle: U[13.62987795707; 2.79883331459]
Coordinates of the inscribed circle: I[8.42987795707; 5.6855283607]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3976988725° = 146°23'49″ = 0.58664831853 rad
∠ B' = β' = 112° = 1.18768238914 rad
∠ C' = γ' = 101.6033011275° = 101°36'11″ = 1.36882855769 rad

How did we calculate this triangle?

1. Input data entered: side a, b and angle β. 2. From angle β, side a and side b we calculate side c - by using the law of cosines and quadratic equation:  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     