# Triangle calculator

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

### Acute scalene triangle.

Sides: a = 34.10987752861   b = 24.76221084339   c = 40

Area: T = 419.9899178284
Perimeter: p = 98.87108837201
Semiperimeter: s = 49.435544186

Angle ∠ A = α = 58° = 1.01222909662 rad
Angle ∠ B = β = 38° = 0.66332251158 rad
Angle ∠ C = γ = 84° = 1.46660765717 rad

Height: ha = 24.6266459013
Height: hb = 33.92219238463
Height: hc = 20.99994589142

Median: ma = 28.56109675811
Median: mb = 35.04987342459
Median: mc = 22.09771781639

Inradius: r = 8.49657100105
Circumradius: R = 20.11101655913

Vertex coordinates: A[40; 0] B[0; 0] C[26.87880817178; 20.99994589142]
Centroid: CG[22.29326939059; 76.9998196381]
Coordinates of the circumscribed circle: U[20; 2.10220847053]
Coordinates of the inscribed circle: I[24.67333334261; 8.49657100105]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122° = 1.01222909662 rad
∠ B' = β' = 142° = 0.66332251158 rad
∠ C' = γ' = 96° = 1.46660765717 rad

# How did we calculate this triangle?

### 1. Input data entered: side c, angle α and angle β. ### 2. From angle α and angle β we calculate angle γ: ### 3. From angle α, angle γ and side c we calculate side a - By using the law of sines, we calculate unknown side a: ### 4. 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. ### 5. The triangle circumference is the sum of the lengths of its three sides ### 6. Semiperimeter of the triangle ### 7. The triangle area using Heron's formula ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle using a Law of Cosines    