Triangle calculator

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

Obtuse scalene triangle.

Sides: a = 12.7   b = 9.31986327517   c = 5.8

Area: T = 25.0243823236
Perimeter: p = 27.81986327517
Semiperimeter: s = 13.90993163759

Angle ∠ A = α = 112.1832799719° = 112°10'58″ = 1.95879592192 rad
Angle ∠ B = β = 42.8° = 42°48' = 0.74770009199 rad
Angle ∠ C = γ = 25.01772002808° = 25°1'2″ = 0.43766325145 rad

Height: ha = 3.94107595647
Height: hb = 5.37107070345
Height: hc = 8.62989045641

Median: ma = 4.46327299023
Median: mb = 8.70437791165
Median: mc = 10.75442297809

Inradius: r = 1.79990692396
Circumradius: R = 6.85875701045

Vertex coordinates: A[5.8; 0] B[0; 0] C[9.31883692792; 8.62989045641]
Centroid: CG[5.03994564264; 2.87663015214]
Coordinates of the circumscribed circle: U[2.9; 6.21441988814]
Coordinates of the inscribed circle: I[4.59106836241; 1.79990692396]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 67.81772002808° = 67°49'2″ = 1.95879592192 rad
∠ B' = β' = 137.2° = 137°12' = 0.74770009199 rad
∠ C' = γ' = 154.9832799719° = 154°58'58″ = 0.43766325145 rad

How did we calculate this triangle?

1. Input data entered: side a, c and angle β. 2. 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. 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     