# Triangle calculator

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

### Right scalene triangle.

Sides: a = 1785.947713048   b = 683.4522377916   c = 1650

Area: T = 563848.212178
Perimeter: p = 4119.43995084
Semiperimeter: s = 2059.76997542

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 22.5° = 22°30' = 0.39326990817 rad
Angle ∠ C = γ = 67.5° = 67°30' = 1.17880972451 rad

Height: ha = 631.4287663402
Height: hb = 1650
Height: hc = 683.4522377916

Median: ma = 892.9743565241
Median: mb = 1685.015536735
Median: mc = 1071.323261849

Vertex coordinates: A[1650; 0] B[0; 0] C[1650; 683.4522377916]
Centroid: CG[1100; 227.8177459305]
Coordinates of the circumscribed circle: U[825; 341.7266188958]
Coordinates of the inscribed circle: I[1376.247737628; 273.7532623717]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 157.5° = 157°30' = 0.39326990817 rad
∠ C' = γ' = 112.5° = 112°30' = 1.17880972451 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    