# Triangle calculator - result

Please enter what you know about the triangle:
You have entered side a, area S and angle β.

### Obtuse scalene triangle.

Sides: a = 3   b = 16.26601938325   c = 18.93296126652

Area: T = 12
Perimeter: p = 38.19898064977
Semiperimeter: s = 19.09549032489

Angle ∠ A = α = 4.4722058555° = 4°28'19″ = 0.07880521461 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 150.5287941445° = 150°31'41″ = 2.62772081945 rad

Height: ha = 8
Height: hb = 1.47659971651
Height: hc = 1.26878547852

Median: ma = 17.58215832496
Median: mb = 10.8432815223
Median: mc = 6.86439924841

Inradius: r = 0.62884399477
Circumradius: R = 19.23774481944

Vertex coordinates: A[18.93296126652; 0] B[0; 0] C[2.71989233611; 1.26878547852]
Centroid: CG[7.21661786754; 0.42326182617]
Coordinates of the circumscribed circle: U[9.46548063326; -16.74880403068]
Coordinates of the inscribed circle: I[2.83547094164; 0.62884399477]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5287941445° = 175°31'41″ = 0.07880521461 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 29.4722058555° = 29°28'19″ = 2.62772081945 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, angle β and area S. ### 2. From side a and angle β we calculate height hc: ### 3. From area T and side a we calculate height ha - The area of the triangle is the product of the length of the base and the height divided by two: ### 4. From area T, side a and angle β we calculate side c: ### 5. From area T, side a and side c we calculate side b - using Heron's formula for the area and solve of the bikvadratic equation:  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. ### 6. The triangle circumference is the sum of the lengths of its three sides ### 7. Semiperimeter of the triangle ### 8. The triangle area using Heron's formula ### 9. Calculate the heights of the triangle from its area. ### 10. Calculation of the inner angles of the triangle using a Law of Cosines    