# Triangle calculator

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

Triangle has two solutions: a=43.00549729383; b=80; c=56 and a=75.89881991381; b=80; c=56.

### #1 Obtuse scalene triangle.

Sides: a = 43.00549729383   b = 80   c = 56

Area: T = 1151.038774475
Perimeter: p = 179.0054972938
Semiperimeter: s = 89.50224864692

Angle ∠ A = α = 30.92110281362° = 30°55'16″ = 0.54396737491 rad
Angle ∠ B = β = 107.0798971864° = 107°4'44″ = 1.86988806187 rad
Angle ∠ C = γ = 42° = 0.73330382858 rad

Height: ha = 53.53304485087
Height: hb = 28.77659436187
Height: hc = 41.10884908838

Median: ma = 65.61773991838
Median: mb = 29.87883173675
Median: mc = 57.79989087156

Inradius: r = 12.86603996398
Circumradius: R = 41.84553433962

Vertex coordinates: A[56; 0] B[0; 0] C[-12.63301098444; 41.10884908838]
Centroid: CG[14.45766300519; 13.70328302946]
Coordinates of the circumscribed circle: U[28; 31.09771504152]
Coordinates of the inscribed circle: I[9.50224864692; 12.86603996398]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.0798971864° = 149°4'44″ = 0.54396737491 rad
∠ B' = β' = 72.92110281362° = 72°55'16″ = 1.86988806187 rad
∠ C' = γ' = 138° = 0.73330382858 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 Acute scalene triangle.

Sides: a = 75.89881991381   b = 80   c = 56

Area: T = 2031.432232043
Perimeter: p = 211.8988199138
Semiperimeter: s = 105.9499099569

Angle ∠ A = α = 65.07989718638° = 65°4'44″ = 1.13658423328 rad
Angle ∠ B = β = 72.92110281362° = 72°55'16″ = 1.27327120349 rad
Angle ∠ C = γ = 42° = 0.73330382858 rad

Height: ha = 53.53304485087
Height: hb = 50.78658080108
Height: hc = 72.55111543011

Median: ma = 57.68876576219
Median: mb = 53.3699170091
Median: mc = 72.77554650703

Inradius: r = 19.1743662907
Circumradius: R = 41.84553433962

Vertex coordinates: A[56; 0] B[0; 0] C[22.29105056464; 72.55111543011]
Centroid: CG[26.09768352155; 24.18437181004]
Coordinates of the circumscribed circle: U[28; 31.09771504152]
Coordinates of the inscribed circle: I[25.9499099569; 19.1743662907]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.9211028136° = 114°55'16″ = 1.13658423328 rad
∠ B' = β' = 107.0798971864° = 107°4'44″ = 1.27327120349 rad
∠ C' = γ' = 138° = 0.73330382858 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    