Triangle calculator

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

Acute scalene triangle.

Sides: a = 191.412155857   b = 146.2   c = 209.3

Area: T = 13533.9398542
Perimeter: p = 546.912155857
Semiperimeter: s = 273.4565779285

Angle ∠ A = α = 62.2° = 62°12' = 1.08655947947 rad
Angle ∠ B = β = 42.50440454849° = 42°30'15″ = 0.74218355391 rad
Angle ∠ C = γ = 75.29659545151° = 75°17'45″ = 1.31441623197 rad

Height: ha = 141.4121925624
Height: hb = 185.1432798113
Height: hc = 129.3265738576

Median: ma = 153.0711450021
Median: mb = 186.75987411
Median: mc = 134.368811332

Inradius: r = 49.4922238114
Circumradius: R = 108.193335026

Vertex coordinates: A[209.3; 0] B[0; 0] C[141.1144273182; 129.3265738576]
Centroid: CG[116.8054757727; 43.10985795255]
Coordinates of the circumscribed circle: U[104.65; 27.4622311274]
Coordinates of the inscribed circle: I[127.2565779285; 49.4922238114]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.8° = 117°48' = 1.08655947947 rad
∠ B' = β' = 137.4965954515° = 137°29'45″ = 0.74218355391 rad
∠ C' = γ' = 104.7044045485° = 104°42'15″ = 1.31441623197 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     