# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 0.21550320573   b = 0.31112306764   c = 0.5

Area: T = 0.02201381066
Perimeter: p = 1.02662627337
Semiperimeter: s = 0.51331313668

Angle ∠ A = α = 15° = 0.26217993878 rad
Angle ∠ B = β = 22° = 0.38439724354 rad
Angle ∠ C = γ = 143° = 2.49658208304 rad

Height: ha = 0.18773032967
Height: hb = 0.12994095226
Height: hc = 0.08105524265

Median: ma = 0.40223339043
Median: mb = 0.35219989479
Median: mc = 0.09551402112

Inradius: r = 0.03992455186
Circumradius: R = 0.41554100353

Vertex coordinates: A[0.5; 0] B[0; 0] C[0.19993742518; 0.08105524265]
Centroid: CG[0.23331247506; 0.02768508088]
Coordinates of the circumscribed circle: U[0.25; -0.33217612054]
Coordinates of the inscribed circle: I[0.20219006905; 0.03992455186]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165° = 0.26217993878 rad
∠ B' = β' = 158° = 0.38439724354 rad
∠ C' = γ' = 37° = 2.49658208304 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    