# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 74   b = 107.5865992753   c = 47

Area: T = 1441.696633867
Perimeter: p = 228.5865992753
Semiperimeter: s = 114.2932996376

Angle ∠ A = α = 34.76662786953° = 34°45'59″ = 0.60767860319 rad
Angle ∠ B = β = 124° = 2.16442082725 rad
Angle ∠ C = γ = 21.23437213047° = 21°14'1″ = 0.37105983492 rad

Height: ha = 38.96547659101
Height: hb = 26.80108186157
Height: hc = 61.34987803691

Median: ma = 74.31660340591
Median: mb = 30.8032817093
Median: mc = 89.29223452389

Inradius: r = 12.61440392184
Circumradius: R = 64.88660777328

Vertex coordinates: A[47; 0] B[0; 0] C[-41.38802748568; 61.34987803691]
Centroid: CG[1.87332417144; 20.45495934564]
Coordinates of the circumscribed circle: U[23.5; 60.48110142404]
Coordinates of the inscribed circle: I[6.70770036237; 12.61440392184]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2343721305° = 145°14'1″ = 0.60767860319 rad
∠ B' = β' = 56° = 2.16442082725 rad
∠ C' = γ' = 158.7666278695° = 158°45'59″ = 0.37105983492 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    