Triangle calculator - result

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

Obtuse scalene triangle.

Sides: a = 10   b = 15.2498529258   c = 7.64327677116

Area: T = 33.42325762884
Perimeter: p = 32.89112969696
Semiperimeter: s = 16.44656484848

Angle ∠ A = α = 35° = 0.61108652382 rad
Angle ∠ B = β = 119° = 2.07769418099 rad
Angle ∠ C = γ = 26° = 0.45437856055 rad

Height: ha = 6.68545152577
Height: hb = 4.38437114679
Height: hc = 8.74661970714

Median: ma = 10.97656444646
Median: mb = 4.59109190816
Median: mc = 12.31548628775

Inradius: r = 2.03223051608
Circumradius: R = 8.71772339781

Vertex coordinates: A[7.64327677116; 0] B[0; 0] C[-4.84880962025; 8.74661970714]
Centroid: CG[0.93215571697; 2.91553990238]
Coordinates of the circumscribed circle: U[3.82113838558; 7.83549979997]
Coordinates of the inscribed circle: I[1.19771192268; 2.03223051608]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145° = 0.61108652382 rad
∠ B' = β' = 61° = 2.07769418099 rad
∠ C' = γ' = 154° = 0.45437856055 rad

How did we calculate this triangle?

1. Input data entered: side a, angle α and angle γ. 2. From angle α and angle γ we calculate angle β: 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     