# 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 = 2.87991632528   b = 1.10218080759   c = 2.66

Area: T = 1.4655404741
Perimeter: p = 6.64109713287
Semiperimeter: s = 3.32204856643

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 = 1.01879379301
Height: hb = 2.66
Height: hc = 1.10218080759

Median: ma = 1.44395816264
Median: mb = 2.71664490165
Median: mc = 1.72771019183

Inradius: r = 0.44113224116
Circumradius: R = 1.44395816264

Vertex coordinates: A[2.66; 0] B[0; 0] C[2.66; 1.10218080759]
Centroid: CG[1.77333333333; 0.36772693586]
Coordinates of the circumscribed circle: U[1.33; 0.5510904038]
Coordinates of the inscribed circle: I[2.21986775884; 0.44113224116]

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    