# Triangle calculator

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

Triangle has two solutions: a=15.8; b=43.72; c=40.17768308898 and a=15.8; b=43.72; c=41.3622107543.

### #1 Obtuse scalene triangle.

Sides: a = 15.8   b = 43.72   c = 40.17768308898

Area: T = 317.1743611487
Perimeter: p = 99.69768308898
Semiperimeter: s = 49.84884154449

Angle ∠ A = α = 21.17° = 21°10'12″ = 0.36994862026 rad
Angle ∠ B = β = 92.15495975958° = 92°8'59″ = 1.60883138824 rad
Angle ∠ C = γ = 66.68804024042° = 66°40'49″ = 1.16437925685 rad

Height: ha = 40.1498558416
Height: hb = 14.50993143407
Height: hc = 15.78988815251

Median: ma = 41.23658832835
Median: mb = 21.30884319032
Median: mc = 26.0199123062

Inradius: r = 6.36327621592
Circumradius: R = 21.87553937352

Vertex coordinates: A[40.17768308898; 0] B[0; 0] C[-0.59326383266; 15.78988815251]
Centroid: CG[13.19547308544; 5.26329605084]
Coordinates of the circumscribed circle: U[20.08884154449; 8.66595852085]
Coordinates of the inscribed circle: I[6.12884154449; 6.36327621592]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.83° = 158°49'48″ = 0.36994862026 rad
∠ B' = β' = 87.85504024042° = 87°51'1″ = 1.60883138824 rad
∠ C' = γ' = 113.3219597596° = 113°19'11″ = 1.16437925685 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 = 15.8   b = 43.72   c = 41.3622107543

Area: T = 326.5310707812
Perimeter: p = 100.8822107543
Semiperimeter: s = 50.44110537715

Angle ∠ A = α = 21.17° = 21°10'12″ = 0.36994862026 rad
Angle ∠ B = β = 87.85504024042° = 87°51'1″ = 1.53332787712 rad
Angle ∠ C = γ = 70.98795975958° = 70°58'47″ = 1.23988276798 rad

Height: ha = 41.33330009889
Height: hb = 14.93773608331
Height: hc = 15.78988815251

Median: ma = 41.81877135936
Median: mb = 22.41436648096
Median: mc = 25.55106010673

Inradius: r = 6.47435108289
Circumradius: R = 21.87553937352

Vertex coordinates: A[41.3622107543; 0] B[0; 0] C[0.59326383266; 15.78988815251]
Centroid: CG[13.98549152899; 5.26329605084]
Coordinates of the circumscribed circle: U[20.68110537715; 7.12992963166]
Coordinates of the inscribed circle: I[6.72110537715; 6.47435108289]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.83° = 158°49'48″ = 0.36994862026 rad
∠ B' = β' = 92.15495975958° = 92°8'59″ = 1.53332787712 rad
∠ C' = γ' = 109.0220402404° = 109°1'13″ = 1.23988276798 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    