# Triangle calculator

You have entered side c, angle α and angle β.

### Right scalene triangle.

Sides: a = 36.58773301719   b = 17.73878896465   c = 32

Area: T = 283.8066234344
Perimeter: p = 86.32552198184
Semiperimeter: s = 43.16326099092

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 29° = 0.50661454831 rad
Angle ∠ C = γ = 61° = 1.06546508437 rad

Height: ha = 15.51439078479
Height: hb = 32
Height: hc = 17.73878896465

Median: ma = 18.2943665086
Median: mb = 33.20662973286
Median: mc = 23.88879201504

Vertex coordinates: A[32; 0] B[0; 0] C[32; 17.73878896465]
Centroid: CG[21.33333333333; 5.91326298822]
Coordinates of the circumscribed circle: U[16; 8.86989448232]
Coordinates of the inscribed circle: I[25.42547202627; 6.57552797373]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 151° = 0.50661454831 rad
∠ C' = γ' = 119° = 1.06546508437 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    