# Triangle calculator

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

### Right scalene triangle.

Sides: a = 12.7   b = 72   c = 73.1111490205

Area: T = 457.2
Perimeter: p = 157.8111490205
Semiperimeter: s = 78.90657451025

Angle ∠ A = α = 10.00334400836° = 10°12″ = 0.1754592966 rad
Angle ∠ B = β = 79.99765599164° = 79°59'48″ = 1.39662033608 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 72
Height: hb = 12.7
Height: hc = 12.50769260309

Median: ma = 72.27994749566
Median: mb = 38.17444679072
Median: mc = 36.55657451025

Inradius: r = 5.79442548975
Circumradius: R = 36.55657451025

Vertex coordinates: A[73.1111490205; 0] B[0; 0] C[2.2066082786; 12.50769260309]
Centroid: CG[25.10658576637; 4.16989753436]
Coordinates of the circumscribed circle: U[36.55657451025; 0]
Coordinates of the inscribed circle: I[6.90657451025; 5.79442548975]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.9976559916° = 169°59'48″ = 0.1754592966 rad
∠ B' = β' = 100.0033440084° = 100°12″ = 1.39662033608 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle γ. ### 2. Calculation of the third side c 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    