# Triangle calculator

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

Triangle has two solutions: a=3.894395228; b=45; c=42 and a=67.02770155446; b=45; c=42.

### #1 Obtuse scalene triangle.

Sides: a = 3.894395228   b = 45   c = 42

Area: T = 53.94105191246
Perimeter: p = 90.894395228
Semiperimeter: s = 45.447697614

Angle ∠ A = α = 3.27222167114° = 3°16'20″ = 0.05771109555 rad
Angle ∠ B = β = 138.7287783289° = 138°43'40″ = 2.42112565824 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 27.70547663897
Height: hb = 2.39773564055
Height: hc = 2.56985961488

Median: ma = 43.48222870133
Median: mb = 19.57988516563
Median: mc = 24.06441108745

Inradius: r = 1.18768890673
Circumradius: R = 34.11096541551

Vertex coordinates: A[42; 0] B[0; 0] C[-2.92766325672; 2.56985961488]
Centroid: CG[13.02444558109; 0.85661987163]
Coordinates of the circumscribed circle: U[21; 26.87987742761]
Coordinates of the inscribed circle: I[0.447697614; 1.18768890673]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.7287783289° = 176°43'40″ = 0.05771109555 rad
∠ B' = β' = 41.27222167114° = 41°16'20″ = 2.42112565824 rad
∠ C' = γ' = 142° = 0.66332251158 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, c and angle γ. ### 2. From angle γ, side b and side c we calculate side a - 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 Obtuse scalene triangle.

Sides: a = 67.02770155446   b = 45   c = 42

Area: T = 928.484390373
Perimeter: p = 154.0277015545
Semiperimeter: s = 77.01435077723

Angle ∠ A = α = 100.7287783289° = 100°43'40″ = 1.75880314666 rad
Angle ∠ B = β = 41.27222167114° = 41°16'20″ = 0.72203360712 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 27.70547663897
Height: hb = 41.26659512769
Height: hc = 44.21435192252

Median: ma = 27.77330948365
Median: mb = 51.20660582979
Median: mc = 53.08330519696

Inradius: r = 12.05661175641
Circumradius: R = 34.11096541551

Vertex coordinates: A[42; 0] B[0; 0] C[50.37664382479; 44.21435192252]
Centroid: CG[30.79221460826; 14.73878397417]
Coordinates of the circumscribed circle: U[21; 26.87987742761]
Coordinates of the inscribed circle: I[32.01435077723; 12.05661175641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 79.27222167114° = 79°16'20″ = 1.75880314666 rad
∠ B' = β' = 138.7287783289° = 138°43'40″ = 0.72203360712 rad
∠ C' = γ' = 142° = 0.66332251158 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, c and angle γ. ### 2. From angle γ, side b and side c we calculate side a - 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    