# Triangle calculator

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

Triangle has two solutions: a=11.4; b=12.8; c=3.33003475024 and a=11.4; b=12.8; c=10.2665585662.

### #1 Obtuse scalene triangle.

Sides: a = 11.4   b = 12.8   c = 3.33003475024

Area: T = 17.91326618627
Perimeter: p = 27.55003475024
Semiperimeter: s = 13.75501737512

Angle ∠ A = α = 58° = 1.01222909662 rad
Angle ∠ B = β = 107.7887820505° = 107°47'16″ = 1.88112523614 rad
Angle ∠ C = γ = 14.21221794948° = 14°12'44″ = 0.24880493261 rad

Height: ha = 3.14325722566
Height: hb = 2.7998853416
Height: hc = 10.85550156308

Median: ma = 7.40878436011
Median: mb = 5.4288272913
Median: mc = 12.00773696783

Inradius: r = 1.30327225828
Circumradius: R = 6.72113168992

Vertex coordinates: A[3.33003475024; 0] B[0; 0] C[-3.48326190798; 10.85550156308]
Centroid: CG[-0.06107571925; 3.61883385436]
Coordinates of the circumscribed circle: U[1.65501737512; 6.51655987791]
Coordinates of the inscribed circle: I[0.95501737512; 1.30327225828]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122° = 1.01222909662 rad
∠ B' = β' = 72.21221794948° = 72°12'44″ = 1.88112523614 rad
∠ C' = γ' = 165.7887820505° = 165°47'16″ = 0.24880493261 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle α. ### 2. From angle α, side b and side a we calculate side c - by using the law of cosines and quadratic 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. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines   ### 10. Calculation of medians ### #2 Acute scalene triangle.

Sides: a = 11.4   b = 12.8   c = 10.2665585662

Area: T = 55.71765464101
Perimeter: p = 34.4665585662
Semiperimeter: s = 17.2332792831

Angle ∠ A = α = 58° = 1.01222909662 rad
Angle ∠ B = β = 72.21221794948° = 72°12'44″ = 1.26603402922 rad
Angle ∠ C = γ = 49.78878205052° = 49°47'16″ = 0.86989613952 rad

Height: ha = 9.77548327035
Height: hb = 8.70657103766
Height: hc = 10.85550156308

Median: ma = 10.10554997151
Median: mb = 8.75884887105
Median: mc = 10.98797284918

Inradius: r = 3.23331698615
Circumradius: R = 6.72113168992

Vertex coordinates: A[10.2665585662; 0] B[0; 0] C[3.48326190798; 10.85550156308]
Centroid: CG[4.58327349139; 3.61883385436]
Coordinates of the circumscribed circle: U[5.1332792831; 4.33994168517]
Coordinates of the inscribed circle: I[4.4332792831; 3.23331698615]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122° = 1.01222909662 rad
∠ B' = β' = 107.7887820505° = 107°47'16″ = 1.26603402922 rad
∠ C' = γ' = 130.2122179495° = 130°12'44″ = 0.86989613952 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle α. ### 2. From angle α, side b and side a we calculate side c - by using the law of cosines and quadratic 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. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines    