# Triangle calculator

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

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    