# Triangle calculator

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

### Right scalene triangle.

Sides: a = 3.27876944458   b = 0.70994229205   c = 3.2

Area: T = 1.13550766727
Perimeter: p = 7.18771173663
Semiperimeter: s = 3.59435586831

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 12.5° = 12°30' = 0.21881661565 rad
Angle ∠ C = γ = 77.5° = 77°30' = 1.35326301703 rad

Height: ha = 0.69326067646
Height: hb = 3.2
Height: hc = 0.70994229205

Median: ma = 1.63988472229
Median: mb = 3.22195993881
Median: mc = 1.75502230944

Inradius: r = 0.31658642373
Circumradius: R = 1.63988472229

Vertex coordinates: A[3.2; 0] B[0; 0] C[3.2; 0.70994229205]
Centroid: CG[2.13333333333; 0.23664743068]
Coordinates of the circumscribed circle: U[1.6; 0.35547114602]
Coordinates of the inscribed circle: I[2.88441357627; 0.31658642373]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 167.5° = 167°30' = 0.21881661565 rad
∠ C' = γ' = 102.5° = 102°30' = 1.35326301703 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    