# Triangle calculator

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

Triangle has two solutions: a=39.8; b=27.5; c=20.13876781907 and a=39.8; b=27.5; c=41.1076526391.

### #1 Obtuse scalene triangle.

Sides: a = 39.8   b = 27.5   c = 20.13876781907

Area: T = 255.9879684879
Perimeter: p = 87.43876781907
Semiperimeter: s = 43.71988390953

Angle ∠ A = α = 112.4111242703° = 112°24'40″ = 1.96219463014 rad
Angle ∠ B = β = 39.7° = 39°42' = 0.6932895713 rad
Angle ∠ C = γ = 27.88987572966° = 27°53'20″ = 0.48767506391 rad

Height: ha = 12.86333007477
Height: hb = 18.61767043549
Height: hc = 25.42329591371

Median: ma = 13.59769864844
Median: mb = 28.38552169528
Median: mc = 32.6921948233

Inradius: r = 5.8555134541
Circumradius: R = 21.5265818338

Vertex coordinates: A[20.13876781907; 0] B[0; 0] C[30.62221022909; 25.42329591371]
Centroid: CG[16.92199268272; 8.47443197124]
Coordinates of the circumscribed circle: U[10.06988390953; 19.02657545026]
Coordinates of the inscribed circle: I[16.21988390953; 5.8555134541]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 67.58987572966° = 67°35'20″ = 1.96219463014 rad
∠ B' = β' = 140.3° = 140°18' = 0.6932895713 rad
∠ C' = γ' = 152.1111242703° = 152°6'40″ = 0.48767506391 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b 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 = 39.8   b = 27.5   c = 41.1076526391

Area: T = 522.5254770354
Perimeter: p = 108.4076526391
Semiperimeter: s = 54.20332631955

Angle ∠ A = α = 67.58987572966° = 67°35'20″ = 1.18796463522 rad
Angle ∠ B = β = 39.7° = 39°42' = 0.6932895713 rad
Angle ∠ C = γ = 72.71112427034° = 72°42'40″ = 1.26990505884 rad

Height: ha = 26.25875261485
Height: hb = 38.00218014803
Height: hc = 25.42329591371

Median: ma = 28.75774034984
Median: mb = 38.05503712987
Median: mc = 27.3444256655

Inradius: r = 9.64400980227
Circumradius: R = 21.5265818338

Vertex coordinates: A[41.1076526391; 0] B[0; 0] C[30.62221022909; 25.42329591371]
Centroid: CG[23.9109542894; 8.47443197124]
Coordinates of the circumscribed circle: U[20.55332631955; 6.39772046345]
Coordinates of the inscribed circle: I[26.70332631955; 9.64400980227]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.4111242703° = 112°24'40″ = 1.18796463522 rad
∠ B' = β' = 140.3° = 140°18' = 0.6932895713 rad
∠ C' = γ' = 107.2898757297° = 107°17'20″ = 1.26990505884 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle β. ### 2. From angle β, side a and side b 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    