Triangle calculator - result

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

Obtuse scalene triangle.

Sides: a = 3   b = 1.34992228812   c = 2.25774619579

Area: T = 1.43110669729
Perimeter: p = 6.60766848391
Semiperimeter: s = 3.30333424195

Angle ∠ A = α = 110° = 1.92198621772 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 0.95440446486
Height: hb = 2.12113203436
Height: hc = 1.26878547852

Median: ma = 1.09992126442
Median: mb = 2.5687677287
Median: mc = 2.03437570083

Inradius: r = 0.43332178718
Circumradius: R = 1.59662666587

Vertex coordinates: A[2.25774619579; 0] B[0; 0] C[2.71989233611; 1.26878547852]
Centroid: CG[1.65987951063; 0.42326182617]
Coordinates of the circumscribed circle: U[1.1298730979; 1.1298730979]
Coordinates of the inscribed circle: I[1.95441195384; 0.43332178718]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 70° = 1.92198621772 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 135° = 0.78553981634 rad

How did we calculate this triangle?

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